Mass-conserving weak solutions to the continuous nonlinear fragmentation equation in the presence of mass transfer
A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the existence of mass-conserving weak solutions to the nonlinear fragmentation equation with mass transfer for collision kernels of the form Φ(x,y)=κ...
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| Published in | Nonlinear analysis: real world applications Vol. 85; p. 104381 |
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| Language | English |
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01.10.2025
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| ISSN | 1468-1218 |
| DOI | 10.1016/j.nonrwa.2025.104381 |
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| Abstract | A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the existence of mass-conserving weak solutions to the nonlinear fragmentation equation with mass transfer for collision kernels of the form Φ(x,y)=κ(xσ1yσ2+yσ1xσ2), κ>0, 0≤σ1≤σ2≤1, and σ1≠1 for (x,y)∈R+2, with integrable daughter distribution functions, thereby extending previous results obtained by Giri & Laurençot (2021). In particular, the existence of at least one global weak solution is shown when the collision kernel exhibits at least linear growth, and one local weak solution when the collision kernel exhibits sublinear growth. In both cases, finite superlinear moment bounds are obtained for positive times without requiring the finiteness of initial superlinear moments. Additionally, the uniqueness of solutions is confirmed in both cases. |
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| AbstractList | A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the existence of mass-conserving weak solutions to the nonlinear fragmentation equation with mass transfer for collision kernels of the form Φ(x,y)=κ(xσ1yσ2+yσ1xσ2), κ>0, 0≤σ1≤σ2≤1, and σ1≠1 for (x,y)∈R+2, with integrable daughter distribution functions, thereby extending previous results obtained by Giri & Laurençot (2021). In particular, the existence of at least one global weak solution is shown when the collision kernel exhibits at least linear growth, and one local weak solution when the collision kernel exhibits sublinear growth. In both cases, finite superlinear moment bounds are obtained for positive times without requiring the finiteness of initial superlinear moments. Additionally, the uniqueness of solutions is confirmed in both cases. |
| ArticleNumber | 104381 |
| Author | Giri, Ankik Kumar Jaiswal, Ram Gopal |
| Author_xml | – sequence: 1 givenname: Ram Gopal orcidid: 0009-0003-8675-1517 surname: Jaiswal fullname: Jaiswal, Ram Gopal – sequence: 2 givenname: Ankik Kumar orcidid: 0000-0002-6339-4647 surname: Giri fullname: Giri, Ankik Kumar email: ankik.giri@ma.iitr.ac.in |
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| Cites_doi | 10.1103/PhysRevE.68.021102 10.1103/PhysRevLett.60.2450 10.1016/j.anihpc.2004.06.001 10.1016/j.jde.2024.05.020 10.1002/mma.1670110505 10.1016/j.physd.2006.07.025 10.1016/j.jcis.2006.08.005 10.1175/1520-0469(1988)045<3387:EORSPI>2.0.CO;2 10.1088/0305-4470/23/7/028 10.1137/20M1386852 10.1093/mnras/stae2039 10.1088/0305-4470/24/12/020 10.1016/j.jcis.2006.05.066 10.1137/23M159130X 10.1016/0009-2509(72)85079-6 10.1088/0305-4470/20/7/033 10.1175/1520-0469(1976)033<2007:EORSWC>2.0.CO;2 10.1002/mma.301 10.1016/S0246-0203(00)01073-6 10.1088/0305-4470/33/6/309 10.1016/S0304-4149(03)00045-0 10.3934/dcds.2020272 10.1016/j.jde.2021.01.043 10.1137/1106036 10.1142/S0218202504003325 10.1007/BF01012594 10.1103/PhysRevLett.58.892 10.1002/mma.310 10.1088/1751-8113/40/17/F03 |
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A doi: 10.1088/1751-8113/40/17/F03 – year: 2019 ident: 10.1016/j.nonrwa.2025.104381_b19 – year: 2024 ident: 10.1016/j.nonrwa.2025.104381_b26 |
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| Snippet | A mathematical model for the continuous nonlinear fragmentation equation is considered in the presence of mass transfer. In this paper, we demonstrate the... |
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| StartPage | 104381 |
| SubjectTerms | Collision-induced breakage Conservation of mass Existence Nonlinear fragmentation Uniqueness |
| Title | Mass-conserving weak solutions to the continuous nonlinear fragmentation equation in the presence of mass transfer |
| URI | https://dx.doi.org/10.1016/j.nonrwa.2025.104381 |
| Volume | 85 |
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