Large time behavior for a Hamilton-Jacobi equation in a critical Coagulation-Fragmentation model
Abstract
We study the large time behavior of the sublinear viscosity solution to a singular Hamilton-Jacobi equation that appears in a critical Coagulation-Fragmentation model with multiplicative coagulation and constant fragmentation kernels. Our results include complete characterizations of stationary solutions and optimal conditions to guarantee large time convergence. In particular, we obtain convergence results under certain natural conditions on the initial data, and a nonconvergence result when such conditions fail.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.13619
- arXiv:
- arXiv:2004.13619
- Bibcode:
- 2020arXiv200413619M
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35B40;
- 35D40;
- 35F21;
- 44A10;
- 45J05;
- 49L20;
- 49L25
- E-Print:
- Change format, updating typos and bibliography