On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions
This paper studies a Caginalp phase-field transition system endowed with a general regular potential, as well as a general class, in both unknown functions, of nonlinear and non-homogeneous (depending on time and space variables) boundary conditions. We first prove the existence, uniqueness and regu...
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| Published in | Nonlinear analysis Vol. 113; pp. 190 - 208 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.01.2015
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| Online Access | Get full text |
| ISSN | 0362-546X 1873-5215 |
| DOI | 10.1016/j.na.2014.10.003 |
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| Abstract | This paper studies a Caginalp phase-field transition system endowed with a general regular potential, as well as a general class, in both unknown functions, of nonlinear and non-homogeneous (depending on time and space variables) boundary conditions. We first prove the existence, uniqueness and regularity of solutions to the Allen–Cahn equation, subject to the nonlinear and non-homogeneous dynamic boundary conditions. The existence, uniqueness and regularity of solutions to the Caginalp system in this new formulation are also proved. This extends previous works concerned with regular potential and nonlinear boundary conditions, allowing the present mathematical model to better approximate the real physical phenomena, especially phase transitions. |
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| AbstractList | This paper studies a Caginalp phase-field transition system endowed with a general regular potential, as well as a general class, in both unknown functions, of nonlinear and non-homogeneous (depending on time and space variables) boundary conditions. We first prove the existence, uniqueness and regularity of solutions to the Allen–Cahn equation, subject to the nonlinear and non-homogeneous dynamic boundary conditions. The existence, uniqueness and regularity of solutions to the Caginalp system in this new formulation are also proved. This extends previous works concerned with regular potential and nonlinear boundary conditions, allowing the present mathematical model to better approximate the real physical phenomena, especially phase transitions. |
| Author | Moroşanu, Costică Miranville, Alain Cârjă, Ovidiu |
| Author_xml | – sequence: 1 givenname: Ovidiu surname: Cârjă fullname: Cârjă, Ovidiu organization: University of Iaşi, 700506 Iaşi, Romania – sequence: 2 givenname: Alain surname: Miranville fullname: Miranville, Alain organization: Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348, SP2MI, 86962 Chasseneuil Futuroscope Cedex, France – sequence: 3 givenname: Costică surname: Moroşanu fullname: Moroşanu, Costică email: costica.morosanu@uaic.ro organization: University of Iaşi, 700506 Iaşi, Romania |
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| Cites_doi | 10.1080/01630569208816458 10.1007/s10957-010-9742-x 10.1002/mma.590 10.1016/0167-2789(90)90015-H 10.1017/S0956792598003520 10.1016/0362-546X(94)90235-6 10.1006/jmaa.1999.6467 10.1016/j.jmaa.2008.01.077 10.1137/S0036142997331669 |
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| Keywords | Nonlinear initial–boundary value problems 80A22 35K61 Nemytskii’s operator Dynamic boundary conditions Leray–Schauder principle Phase-field models Thermodynamics 47H30 Nonlinear parabolic systems 35Q56 74A15 35B65 |
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| References | Barrett, Blowey, Garcke (br000005) 1999; 37 Elliott, Zheng (br000035) 1990; vol. 95 Benincasa, Favini, Moroşanu (br000010) 2011; 148 Blowey, Elliott (br000020) 1994 Moroşanu, Motreanu (br000090) 2000; 2 Hoffman, Jiang (br000045) 1992; 13 Miranville, Zelik (br000070) 2005; 28 Ladyzhenskaya, Solonnikov, Uraltzava (br000060) 1968 Fonseca, Gangbo (br000040) 1995 Kenmochi, Niezgódka (br000055) 1994; 22 Moroşanu, Motreanu (br000085) 2000; 1 Penrose, Fife (br000095) 1990; 43 Iorga, Moroşanu, Tofan (br000050) 2009; XIV Moroşanu, Motreanu (br000080) 1999; 237 Bird, Stewart, Lightfoot (br000015) 2002 Caginalp, Chen (br000025) 1998; 9 Cherfils, Gatti, Miranville (br000030) 2008; 343 Lions (br000065) 1985 Moroşanu (br000075) 2012 Fonseca (10.1016/j.na.2014.10.003_br000040) 1995 Lions (10.1016/j.na.2014.10.003_br000065) 1985 Moroşanu (10.1016/j.na.2014.10.003_br000090) 2000; 2 Elliott (10.1016/j.na.2014.10.003_br000035) 1990; vol. 95 Benincasa (10.1016/j.na.2014.10.003_br000010) 2011; 148 Penrose (10.1016/j.na.2014.10.003_br000095) 1990; 43 Moroşanu (10.1016/j.na.2014.10.003_br000080) 1999; 237 Caginalp (10.1016/j.na.2014.10.003_br000025) 1998; 9 Bird (10.1016/j.na.2014.10.003_br000015) 2002 Moroşanu (10.1016/j.na.2014.10.003_br000075) 2012 Barrett (10.1016/j.na.2014.10.003_br000005) 1999; 37 Cherfils (10.1016/j.na.2014.10.003_br000030) 2008; 343 Hoffman (10.1016/j.na.2014.10.003_br000045) 1992; 13 Moroşanu (10.1016/j.na.2014.10.003_br000085) 2000; 1 Iorga (10.1016/j.na.2014.10.003_br000050) 2009; XIV Kenmochi (10.1016/j.na.2014.10.003_br000055) 1994; 22 Ladyzhenskaya (10.1016/j.na.2014.10.003_br000060) 1968 Miranville (10.1016/j.na.2014.10.003_br000070) 2005; 28 Blowey (10.1016/j.na.2014.10.003_br000020) 1994 |
| References_xml | – volume: 343 start-page: 557 year: 2008 end-page: 566 ident: br000030 article-title: Existence of global solutions to the Caginalp phase field system with dynamic boundary conditions and singular potentials publication-title: J. Math. Anal. Appl. – volume: vol. 95 start-page: 46 year: 1990 end-page: 58 ident: br000035 article-title: Global existence and stability of solutions to the phase field equations publication-title: Internat. Ser. Numer. Math. – year: 1968 ident: br000060 article-title: Linear and Quasi Linear Equations of Parabolic Type – volume: 13 start-page: 11 year: 1992 end-page: 27 ident: br000045 article-title: Optimal control problem of a phase field model for solidification publication-title: Numer. Funct. Anal. Optim. – volume: 237 start-page: 515 year: 1999 end-page: 540 ident: br000080 article-title: A generalized phase field system publication-title: J. Math. Anal. Appl. – year: 2002 ident: br000015 article-title: Transport Phenomena – volume: 28 start-page: 709 year: 2005 end-page: 735 ident: br000070 article-title: Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions publication-title: Math. Methods Appl. Sci. – volume: 1 start-page: 187 year: 2000 end-page: 204 ident: br000085 article-title: The phase field system with a general nonlinearity publication-title: Int. J. Differ. Equ. Appl. – volume: 2 start-page: 113 year: 2000 end-page: 129 ident: br000090 article-title: Uniqueness and approximation for the nonlinear parabolic equation in Caginalp’s model publication-title: Int. J. Appl. Math. – volume: 9 start-page: 417 year: 1998 end-page: 445 ident: br000025 article-title: Convergence of the phase field model to its sharp interface limits publication-title: European J. Appl. Math. – volume: 148 start-page: 14 year: 2011 end-page: 30 ident: br000010 article-title: A product formula approach to a non-homogeneous boundary optimal control problem governed by nonlinear phase-field transition system. Part I: a phase-field model publication-title: J. Optim. Theory Appl. – year: 2012 ident: br000075 article-title: Analysis and Optimal Control of Phase-Field Transition System: Fractional Steps Methods – volume: 43 start-page: 44 year: 1990 end-page: 62 ident: br000095 article-title: Thermodynamically consistent models of phase-field type for kinetics of phase transitions publication-title: Physica D – volume: 22 start-page: 1163 year: 1994 end-page: 1180 ident: br000055 article-title: Evolution systems of nonlinear variational inequalities arising from phase change problems publication-title: Nonlinear Anal. TMA – start-page: 1 year: 1994 end-page: 22 ident: br000020 article-title: A phase-field model with a double obstacle potential publication-title: Motion by Mean Curvature and Related Topics, Trento—1992 – volume: XIV start-page: 72 year: 2009 end-page: 75 ident: br000050 article-title: Numerical simulation of the thickness accretions in the secondary cooling zone of a continuous casting machine publication-title: Metal. Int. – volume: 37 start-page: 286 year: 1999 end-page: 318 ident: br000005 article-title: Finite element aproximation of the Cahn–Hilliard equation with degenerate mobility publication-title: SIAM J. Numer. Anal. – year: 1985 ident: br000065 article-title: Control of Distributed Singular Systems – year: 1995 ident: br000040 article-title: Degree Theory in Analysis and Applications – volume: 13 start-page: 11 issue: 1–2 year: 1992 ident: 10.1016/j.na.2014.10.003_br000045 article-title: Optimal control problem of a phase field model for solidification publication-title: Numer. Funct. Anal. Optim. doi: 10.1080/01630569208816458 – volume: 148 start-page: 14 issue: 1 year: 2011 ident: 10.1016/j.na.2014.10.003_br000010 article-title: A product formula approach to a non-homogeneous boundary optimal control problem governed by nonlinear phase-field transition system. Part I: a phase-field model publication-title: J. Optim. Theory Appl. doi: 10.1007/s10957-010-9742-x – year: 2012 ident: 10.1016/j.na.2014.10.003_br000075 – volume: vol. 95 start-page: 46 year: 1990 ident: 10.1016/j.na.2014.10.003_br000035 article-title: Global existence and stability of solutions to the phase field equations – year: 1985 ident: 10.1016/j.na.2014.10.003_br000065 – volume: 28 start-page: 709 year: 2005 ident: 10.1016/j.na.2014.10.003_br000070 article-title: Exponential attractors for the Cahn–Hilliard equation with dynamic boundary conditions publication-title: Math. Methods Appl. Sci. doi: 10.1002/mma.590 – volume: 43 start-page: 44 year: 1990 ident: 10.1016/j.na.2014.10.003_br000095 article-title: Thermodynamically consistent models of phase-field type for kinetics of phase transitions publication-title: Physica D doi: 10.1016/0167-2789(90)90015-H – volume: 9 start-page: 417 year: 1998 ident: 10.1016/j.na.2014.10.003_br000025 article-title: Convergence of the phase field model to its sharp interface limits publication-title: European J. Appl. Math. doi: 10.1017/S0956792598003520 – year: 1968 ident: 10.1016/j.na.2014.10.003_br000060 – volume: 22 start-page: 1163 year: 1994 ident: 10.1016/j.na.2014.10.003_br000055 article-title: Evolution systems of nonlinear variational inequalities arising from phase change problems publication-title: Nonlinear Anal. TMA doi: 10.1016/0362-546X(94)90235-6 – volume: 237 start-page: 515 year: 1999 ident: 10.1016/j.na.2014.10.003_br000080 article-title: A generalized phase field system publication-title: J. Math. Anal. Appl. doi: 10.1006/jmaa.1999.6467 – volume: XIV start-page: 72 issue: 1 year: 2009 ident: 10.1016/j.na.2014.10.003_br000050 article-title: Numerical simulation of the thickness accretions in the secondary cooling zone of a continuous casting machine publication-title: Metal. Int. – year: 2002 ident: 10.1016/j.na.2014.10.003_br000015 – start-page: 1 year: 1994 ident: 10.1016/j.na.2014.10.003_br000020 article-title: A phase-field model with a double obstacle potential – volume: 343 start-page: 557 year: 2008 ident: 10.1016/j.na.2014.10.003_br000030 article-title: Existence of global solutions to the Caginalp phase field system with dynamic boundary conditions and singular potentials publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.01.077 – volume: 37 start-page: 286 year: 1999 ident: 10.1016/j.na.2014.10.003_br000005 article-title: Finite element aproximation of the Cahn–Hilliard equation with degenerate mobility publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142997331669 – volume: 2 start-page: 113 issue: 1 year: 2000 ident: 10.1016/j.na.2014.10.003_br000090 article-title: Uniqueness and approximation for the nonlinear parabolic equation in Caginalp’s model publication-title: Int. J. Appl. Math. – volume: 1 start-page: 187 issue: 2 year: 2000 ident: 10.1016/j.na.2014.10.003_br000085 article-title: The phase field system with a general nonlinearity publication-title: Int. J. Differ. Equ. Appl. – year: 1995 ident: 10.1016/j.na.2014.10.003_br000040 |
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| SubjectTerms | Boundary conditions Dynamic boundary conditions Dynamical systems Leray–Schauder principle Mathematical analysis Mathematical models Nemytskii’s operator Nonlinear dynamics Nonlinear initial–boundary value problems Nonlinear parabolic systems Nonlinearity Phase-field models Regularity Thermodynamics Uniqueness |
| Title | On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions |
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