Entire Solutions for Nonlocal Dispersal Equations with Bistable Nonlinearity: Asymmetric Case
This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave spee...
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| Published in | Acta mathematica Sinica. English series Vol. 35; no. 11; pp. 1771 - 1794 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Beijing
Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society
01.11.2019
Springer Nature B.V |
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| Abstract | This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves. We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds. |
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| AbstractList | This paper mainly focuses on the entire solutions of a nonlocal dispersal equation with asymmetric kernel and bistable nonlinearity. Compared with symmetric case, the asymmetry of the dispersal kernel function makes more diverse types of entire solutions since it can affect the sign of the wave speeds and the symmetry of the corresponding nonincreasing and nondecreasing traveling waves. We divide the bistable case into two monostable cases by restricting the range of the variable, and obtain some merging-front entire solutions which behave as the coupling of monostable and bistable waves. Before this, we characterize the classification of the wave speeds so that the entire solutions can be constructed more clearly. Especially, we investigate the influence of the asymmetry of the kernel on the minimal and maximal wave speeds. |
| Author | Sun, Yu Juan Li, Wan Tong Wang, Zhi Cheng Zhang, Li |
| Author_xml | – sequence: 1 givenname: Li surname: Zhang fullname: Zhang, Li organization: School of Science, Chang’an University – sequence: 2 givenname: Wan Tong surname: Li fullname: Li, Wan Tong email: wtli@lzu.edu.cn organization: School of Mathematics and Statistics, Lanzhou University – sequence: 3 givenname: Zhi Cheng surname: Wang fullname: Wang, Zhi Cheng organization: School of Mathematics and Statistics, Lanzhou University – sequence: 4 givenname: Yu Juan surname: Sun fullname: Sun, Yu Juan organization: ISN Laboratory, Xidian University |
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| Cites_doi | 10.1017/S0308210504000721 10.1007/s10884-014-9416-8 10.1007/s00033-007-7005-y 10.1051/mmnp/20138307 10.1016/j.jde.2013.07.049 10.1007/PL00004238 10.2977/prims/1260476648 10.1007/s11425-016-9003-7 10.3934/cpaa.2019051 10.3934/dcds.2015.35.1531 10.1016/j.jde.2008.12.005 10.1016/j.jde.2007.11.002 10.1007/b98869 10.1090/S0002-9939-04-07432-5 10.1016/j.jde.2011.04.020 10.2977/prims/1260476649 10.1090/S0002-9947-08-04694-1 10.1016/j.jde.2004.10.028 10.1137/080727312 10.1016/j.jde.2014.12.013 10.1002/(SICI)1097-0312(199910)52:10<1255::AID-CPA4>3.0.CO;2-W 10.1016/j.jde.2012.04.022 10.1016/j.nonrwa.2009.07.005 10.1016/j.matpur.2008.07.002 10.1016/S0022-0396(03)00170-0 10.3934/dcds.2013.33.921 10.1137/080723715 10.1088/0951-7715/23/7/005 10.2977/prims/1145476150 10.1007/s10884-006-9046-x 10.1016/j.jde.2008.03.023 10.1007/s002050050037 10.1016/j.na.2010.09.032 10.3934/dcds.2005.12.193 |
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| References | Hamel, Nadirashvili (CR14) 2001; 157 Bates (CR1) 2006 Liu, Li, Wang (CR19) 2009; 246 Crooks, Tsai (CR10) 2012; 253 Morita, Tachibana (CR21) 2009; 40 Chen (CR4) 1997; 2 Schumacher (CR24) 1980; 316 Sun, Li, Wang (CR25) 2011; 251 Guo, Morita (CR12) 2005; 12 Yagisita (CR35) 2003; 39 Pan, Li, Lin (CR23) 2009; 60 Yagisita (CR37) 2009; 45 Wang, Lv (CR28) 2010; 23 Wang, Li, Wu (CR30) 2009; 40 Carr, Chmaj (CR3) 2004; 132 Coville, Dupaigne (CR9) 2007; 137 Wang, Li, Ruan (CR31) 2013; 8 Morita, Ninomiya (CR20) 2006; 18 Sun, Li, Wang (CR26) 2011; 74 Li, Sun, Wang (CR15) 2010; 11 Coville (CR6) 2007; 68 Zhang, Li, Wang (CR40) 2017; 60 CR7 Li, Liu, Wang (CR17) 2008; 90 Wu, Ruan (CR32) 2015; 258 Wu, Shi, Yang (CR33) 2013; 255 Li, Wang, Wu (CR16) 2008; 245 Murray (CR22) 2003 Chen, Guo (CR5) 2005; 212 Wu, Sun, Liu (CR34) 2013; 33 Zhang, Li, Wu (CR39) 2016; 28 Wang, Li, Ruan (CR29) 2009; 361 Sun, Zhang, Li (CR27) 2019; 18 Hamel, Nadirashvili (CR13) 1999; 52 Zhang (CR38) 2004; 197 Li, Zhang, Zhang (CR18) 2015; 35 Bates, Fife, Ren (CR2) 1997; 138 Folland (CR11) 1999 Yagisita (CR36) 2009; 45 Coville, Dávila, Martínez (CR8) 2008; 244 Z C Wang (8294_CR29) 2009; 361 H Yagisita (8294_CR36) 2009; 45 W T Li (8294_CR18) 2015; 35 W T Li (8294_CR16) 2008; 245 W T Li (8294_CR17) 2008; 90 Z C Wang (8294_CR30) 2009; 40 P W Bates (8294_CR2) 1997; 138 N W Liu (8294_CR19) 2009; 246 Y Morita (8294_CR20) 2006; 18 Y J Sun (8294_CR26) 2011; 74 J Murray (8294_CR22) 2003 Y J Sun (8294_CR27) 2019; 18 S X Pan (8294_CR23) 2009; 60 J Coville (8294_CR8) 2008; 244 S L Wu (8294_CR33) 2013; 255 P W Bates (8294_CR1) 2006 J Carr (8294_CR3) 2004; 132 K Schumacher (8294_CR24) 1980; 316 Y J Sun (8294_CR25) 2011; 251 M X Wang (8294_CR28) 2010; 23 X F Chen (8294_CR5) 2005; 212 X F Chen (8294_CR4) 1997; 2 F Hamel (8294_CR14) 2001; 157 J Coville (8294_CR6) 2007; 68 L Zhang (8294_CR40) 2017; 60 L H Zhang (8294_CR38) 2004; 197 H Yagisita (8294_CR35) 2003; 39 H Yagisita (8294_CR37) 2009; 45 S L Wu (8294_CR32) 2015; 258 W T Li (8294_CR15) 2010; 11 Z C Wang (8294_CR31) 2013; 8 J S Guo (8294_CR12) 2005; 12 G B Folland (8294_CR11) 1999 S L Wu (8294_CR34) 2013; 33 E C M Crooks (8294_CR10) 2012; 253 J Coville (8294_CR9) 2007; 137 Y Morita (8294_CR21) 2009; 40 L Zhang (8294_CR39) 2016; 28 8294_CR7 F Hamel (8294_CR13) 1999; 52 |
| References_xml | – volume: 68 start-page: 1 year: 2007 end-page: 23 ident: CR6 article-title: Maximum principles, sliding techniques and applications to nonlocal equations publication-title: Electron. J. Differential Equations – volume: 137 start-page: 727 year: 2007 end-page: 755 ident: CR9 article-title: On a nonlocal reaction-diffusion equation arising in population dynamics publication-title: Proc. Roy. Soc. Edinburgh Sect. A doi: 10.1017/S0308210504000721 – year: 1999 ident: CR11 publication-title: Real Analysis: Modern Techniques and their Applications – volume: 28 start-page: 189 year: 2016 end-page: 224 ident: CR39 article-title: Multi-type entire solutions in a nonlocal dispersal epidemic model publication-title: J. Dynam. Differential Equations doi: 10.1007/s10884-014-9416-8 – volume: 60 start-page: 377 year: 2009 end-page: 392 ident: CR23 article-title: Travelling wave fronts in nonlocal reaction-diffusion systems and applications publication-title: Z. Angew. Math. Phys. doi: 10.1007/s00033-007-7005-y – volume: 8 start-page: 78 year: 2013 end-page: 103 ident: CR31 article-title: Entire solutions in lattice delayed differential equations with nonlocal interaction: bistable case publication-title: Math. Model.Nat.Phenom. doi: 10.1051/mmnp/20138307 – volume: 255 start-page: 3505 year: 2013 end-page: 3535 ident: CR33 article-title: Entire solutions in periodic lattice dynamical systems publication-title: J. Differential Equations doi: 10.1016/j.jde.2013.07.049 – volume: 12 start-page: 193 year: 2005 end-page: 212 ident: CR12 article-title: Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations publication-title: Discrete Contin. Dyn. Syst. – volume: 157 start-page: 91 year: 2001 end-page: 163 ident: CR14 article-title: Travelling fronts and entire solutions of the Fisher-KPP equation in publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/PL00004238 – volume: 45 start-page: 925 year: 2009 end-page: 953 ident: CR36 article-title: Existence and nonexistence of traveling waves for a nonlocal monostable equation publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1260476648 – volume: 60 start-page: 1791 year: 2017 end-page: 1804 ident: CR40 article-title: Entire solution in an ignition nonlocal dispersal equation: asymmetric kernel publication-title: Sci. China Ser. A doi: 10.1007/s11425-016-9003-7 – volume: 18 start-page: 1049 issue: 3 year: 2019 end-page: 1072 ident: CR27 article-title: Entire solutions in nonlocal monostable equations: asymmetric case publication-title: Commun. Pure. Appl. Anal. doi: 10.3934/cpaa.2019051 – volume: 35 start-page: 1531 year: 2015 end-page: 1560 ident: CR18 article-title: Invasion entire solutions in a competition system with nonlocal dispersal publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2015.35.1531 – volume: 246 start-page: 4249 year: 2009 end-page: 4267 ident: CR19 article-title: Entire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylinders publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.12.005 – volume: 244 start-page: 3080 year: 2008 end-page: 3118 ident: CR8 article-title: Nonlocal anisotropic dispersal with monostable nonlinearity publication-title: J. Differential Equations doi: 10.1016/j.jde.2007.11.002 – year: 2003 ident: CR22 publication-title: Mathematical Biology doi: 10.1007/b98869 – volume: 132 start-page: 2433 year: 2004 end-page: 2439 ident: CR3 article-title: Uniqueness of travelling waves for nonlocal monostable equations publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-04-07432-5 – volume: 251 start-page: 551 year: 2011 end-page: 581 ident: CR25 article-title: Entire solutions in nonlocal dispersal equations with bistable nonlinearity publication-title: J. Differential Equations doi: 10.1016/j.jde.2011.04.020 – volume: 45 start-page: 955 year: 2009 end-page: 979 ident: CR37 article-title: Existence of traveling waves for a nonlocal bistable equation: an abstract approach publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1260476649 – volume: 361 start-page: 2047 year: 2009 end-page: 2084 ident: CR29 article-title: Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-08-04694-1 – volume: 2 start-page: 125 year: 1997 end-page: 160 ident: CR4 article-title: Existence, uniqueness and asymptotical stability of travelling fronts in non-local evolution equations publication-title: Adv. Differential Equations – volume: 212 start-page: 62 year: 2005 end-page: 84 ident: CR5 article-title: Existence and uniqueness of entire solutions for a reaction-diffusion equation publication-title: J. Differential Equations doi: 10.1016/j.jde.2004.10.028 – volume: 40 start-page: 2392 year: 2009 end-page: 2420 ident: CR30 article-title: Entire solutions in delayed lattice differential equations with monostable nonlinearity publication-title: SIAM J. Math. Anal. doi: 10.1137/080727312 – volume: 258 start-page: 2435 year: 2015 end-page: 2470 ident: CR32 article-title: Entire solutions for nonlocal dispersal equations with spatio-temporal delay: Monostable case publication-title: J. Differential Equations doi: 10.1016/j.jde.2014.12.013 – volume: 316 start-page: 54 year: 1980 end-page: 70 ident: CR24 article-title: Traveling-front solutions for integro-differential equations, I publication-title: J. Reine Angew. Math. – volume: 52 start-page: 1255 year: 1999 end-page: 1276 ident: CR13 article-title: Entire solution of the KPP eqution publication-title: Comm. Pure Appl. Math. doi: 10.1002/(SICI)1097-0312(199910)52:10<1255::AID-CPA4>3.0.CO;2-W – volume: 253 start-page: 1206 year: 2012 end-page: 1249 ident: CR10 article-title: Front-like entire solutions for equations with convection publication-title: J. Differential Equations doi: 10.1016/j.jde.2012.04.022 – volume: 11 start-page: 2302 year: 2010 end-page: 2313 ident: CR15 article-title: Entire solutions in the Fisher-KPP equation with nonlocal dispersal publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2009.07.005 – year: 2006 ident: CR1 article-title: On some nonlocal evolution equations arising in materials science publication-title: Nonlinear Dynamics and Evolution Equations – volume: 90 start-page: 492 year: 2008 end-page: 504 ident: CR17 article-title: Entire solutions in reaction-advection-diffusion equations in cylinders publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2008.07.002 – volume: 197 start-page: 162 year: 2004 end-page: 196 ident: CR38 article-title: Existence, uniqueness and exponential stability of traveling wave solutions of some integral differential equations arising from neuronal networks publication-title: J. Differential Equations doi: 10.1016/S0022-0396(03)00170-0 – volume: 33 start-page: 921 year: 2013 end-page: 946 ident: CR34 article-title: Traveling fronts and entire solutions in partially degenerate reaction-diffusion systems with monostable nonlinearity publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2013.33.921 – ident: CR7 – volume: 40 start-page: 2217 year: 2009 end-page: 2240 ident: CR21 article-title: An entire solution to the Lotka-Volterra competition-diffusion equations publication-title: SIAM J. Math. Anal. doi: 10.1137/080723715 – volume: 23 start-page: 1609 year: 2010 end-page: 1630 ident: CR28 article-title: Entire solutions of a diffusive and competitive Lotka-Volterra type system with nonlocal delays publication-title: Nonlinearity doi: 10.1088/0951-7715/23/7/005 – volume: 39 start-page: 117 year: 2003 end-page: 164 ident: CR35 article-title: Back and global solutions characterizing annihilation dynamics of traveling fronts publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1145476150 – volume: 18 start-page: 841 year: 2006 end-page: 861 ident: CR20 article-title: Entire solutions with merging fronts to reaction-diffusion equations publication-title: J. Dynam. Differential Equations doi: 10.1007/s10884-006-9046-x – volume: 245 start-page: 102 year: 2008 end-page: 129 ident: CR16 article-title: Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.03.023 – volume: 138 start-page: 105 year: 1997 end-page: 136 ident: CR2 article-title: Traveling waves in a convolution model for phase transitions publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050050037 – volume: 74 start-page: 814 year: 2011 end-page: 826 ident: CR26 article-title: Traveling waves for a nonlocal anisotropic dispersal equation with monostable nonlinearity publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.09.032 – volume: 18 start-page: 1049 issue: 3 year: 2019 ident: 8294_CR27 publication-title: Commun. Pure. Appl. Anal. doi: 10.3934/cpaa.2019051 – volume: 18 start-page: 841 year: 2006 ident: 8294_CR20 publication-title: J. Dynam. Differential Equations doi: 10.1007/s10884-006-9046-x – volume: 258 start-page: 2435 year: 2015 ident: 8294_CR32 publication-title: J. Differential Equations doi: 10.1016/j.jde.2014.12.013 – volume-title: Real Analysis: Modern Techniques and their Applications year: 1999 ident: 8294_CR11 – volume: 316 start-page: 54 year: 1980 ident: 8294_CR24 publication-title: J. Reine Angew. Math. – volume: 2 start-page: 125 year: 1997 ident: 8294_CR4 publication-title: Adv. Differential Equations – volume: 23 start-page: 1609 year: 2010 ident: 8294_CR28 publication-title: Nonlinearity doi: 10.1088/0951-7715/23/7/005 – volume: 11 start-page: 2302 year: 2010 ident: 8294_CR15 publication-title: Nonlinear Anal. Real World Appl. doi: 10.1016/j.nonrwa.2009.07.005 – volume-title: Nonlinear Dynamics and Evolution Equations year: 2006 ident: 8294_CR1 – volume: 52 start-page: 1255 year: 1999 ident: 8294_CR13 publication-title: Comm. Pure Appl. Math. doi: 10.1002/(SICI)1097-0312(199910)52:10<1255::AID-CPA4>3.0.CO;2-W – volume: 40 start-page: 2392 year: 2009 ident: 8294_CR30 publication-title: SIAM J. Math. Anal. doi: 10.1137/080727312 – volume: 39 start-page: 117 year: 2003 ident: 8294_CR35 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1145476150 – volume: 45 start-page: 955 year: 2009 ident: 8294_CR37 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1260476649 – volume: 251 start-page: 551 year: 2011 ident: 8294_CR25 publication-title: J. Differential Equations doi: 10.1016/j.jde.2011.04.020 – volume: 245 start-page: 102 year: 2008 ident: 8294_CR16 publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.03.023 – volume: 28 start-page: 189 year: 2016 ident: 8294_CR39 publication-title: J. Dynam. Differential Equations doi: 10.1007/s10884-014-9416-8 – volume: 157 start-page: 91 year: 2001 ident: 8294_CR14 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/PL00004238 – volume: 60 start-page: 1791 year: 2017 ident: 8294_CR40 publication-title: Sci. China Ser. A doi: 10.1007/s11425-016-9003-7 – volume: 74 start-page: 814 year: 2011 ident: 8294_CR26 publication-title: Nonlinear Anal. doi: 10.1016/j.na.2010.09.032 – volume: 137 start-page: 727 year: 2007 ident: 8294_CR9 publication-title: Proc. Roy. Soc. Edinburgh Sect. A doi: 10.1017/S0308210504000721 – volume: 197 start-page: 162 year: 2004 ident: 8294_CR38 publication-title: J. Differential Equations doi: 10.1016/S0022-0396(03)00170-0 – volume: 244 start-page: 3080 year: 2008 ident: 8294_CR8 publication-title: J. Differential Equations doi: 10.1016/j.jde.2007.11.002 – volume: 12 start-page: 193 year: 2005 ident: 8294_CR12 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2005.12.193 – volume: 246 start-page: 4249 year: 2009 ident: 8294_CR19 publication-title: J. Differential Equations doi: 10.1016/j.jde.2008.12.005 – volume: 68 start-page: 1 year: 2007 ident: 8294_CR6 publication-title: Electron. J. Differential Equations – volume: 45 start-page: 925 year: 2009 ident: 8294_CR36 publication-title: Publ. Res. Inst. Math. Sci. doi: 10.2977/prims/1260476648 – volume: 60 start-page: 377 year: 2009 ident: 8294_CR23 publication-title: Z. Angew. Math. Phys. doi: 10.1007/s00033-007-7005-y – volume: 212 start-page: 62 year: 2005 ident: 8294_CR5 publication-title: J. Differential Equations doi: 10.1016/j.jde.2004.10.028 – volume: 138 start-page: 105 year: 1997 ident: 8294_CR2 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s002050050037 – ident: 8294_CR7 – volume: 40 start-page: 2217 year: 2009 ident: 8294_CR21 publication-title: SIAM J. Math. Anal. doi: 10.1137/080723715 – volume: 8 start-page: 78 year: 2013 ident: 8294_CR31 publication-title: Math. Model.Nat.Phenom. doi: 10.1051/mmnp/20138307 – volume: 33 start-page: 921 year: 2013 ident: 8294_CR34 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2013.33.921 – volume: 132 start-page: 2433 year: 2004 ident: 8294_CR3 publication-title: Proc. Amer. Math. Soc. doi: 10.1090/S0002-9939-04-07432-5 – volume: 361 start-page: 2047 year: 2009 ident: 8294_CR29 publication-title: Trans. Amer. Math. Soc. doi: 10.1090/S0002-9947-08-04694-1 – volume-title: Mathematical Biology year: 2003 ident: 8294_CR22 doi: 10.1007/b98869 – volume: 90 start-page: 492 year: 2008 ident: 8294_CR17 publication-title: J. Math. Pures Appl. doi: 10.1016/j.matpur.2008.07.002 – volume: 35 start-page: 1531 year: 2015 ident: 8294_CR18 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2015.35.1531 – volume: 253 start-page: 1206 year: 2012 ident: 8294_CR10 publication-title: J. Differential Equations doi: 10.1016/j.jde.2012.04.022 – volume: 255 start-page: 3505 year: 2013 ident: 8294_CR33 publication-title: J. Differential Equations doi: 10.1016/j.jde.2013.07.049 |
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| SubjectTerms | Asymmetry Kernel functions Mathematical analysis Mathematics Mathematics and Statistics Nonlinearity Symmetry Traveling waves |
| Title | Entire Solutions for Nonlocal Dispersal Equations with Bistable Nonlinearity: Asymmetric Case |
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