A note on global in-time behavior for the semilinear nonlocal heat exchanger system
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912381926375424 |
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| author | Chen, Wenhui Li, Xiaolin Liu, Yan |
| author_facet | Chen, Wenhui Li, Xiaolin Liu, Yan |
| contents | We mainly study global in-time asymptotic behavior for the nonlocal reaction-diffusion system with fractional Laplacians which models dispersal of individuals between two exchanging environments for its diffusive components and incorporates the Fujita-type power nonlinearities for its reactive components. We derive a global in-time existence result in the super-critical case, and large time asymptotic profiles of global in-time solutions in the general $L^m$ framework. As a byproduct, the sharp lower bound estimates of lifespan for local in-time solutions in the sub-critical and critical cases are determined. These results extend the existence part of [S. Tréton, SIAM J. Math. Anal. (2024)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12756 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on global in-time behavior for the semilinear nonlocal heat exchanger system Chen, Wenhui Li, Xiaolin Liu, Yan Analysis of PDEs We mainly study global in-time asymptotic behavior for the nonlocal reaction-diffusion system with fractional Laplacians which models dispersal of individuals between two exchanging environments for its diffusive components and incorporates the Fujita-type power nonlinearities for its reactive components. We derive a global in-time existence result in the super-critical case, and large time asymptotic profiles of global in-time solutions in the general $L^m$ framework. As a byproduct, the sharp lower bound estimates of lifespan for local in-time solutions in the sub-critical and critical cases are determined. These results extend the existence part of [S. Tréton, SIAM J. Math. Anal. (2024)]. |
| title | A note on global in-time behavior for the semilinear nonlocal heat exchanger system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.12756 |