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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2411.12900 |
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| _version_ | 1866912127248236544 |
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| author | Iagar, Razvan Gabriel Sánchez, Ariel |
| author_facet | Iagar, Razvan Gabriel Sánchez, Ariel |
| contents | The following Fisher-KPP type equation $$ u_t=Ku_{xx}-Bu^q+Au^p, \quad (x,t)\in\real\times(0,\infty), $$ with $p>q>0$ and $A$, $B$, $K$ positive coefficients, is considered. For both $p>q>1$ and $p>1$, $q=1$, we construct stationary solutions, establish their behavior as $|x|\to\infty$ and prove that they are separatrices between solutions decreasing to zero in infinite time and solutions presenting blow-up in finite time. We also establish decay rates for the solutions that decay to zero as $t\to\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Qualitative properties of solutions to a generalized Fisher-KPP equation Iagar, Razvan Gabriel Sánchez, Ariel Analysis of PDEs The following Fisher-KPP type equation $$ u_t=Ku_{xx}-Bu^q+Au^p, \quad (x,t)\in\real\times(0,\infty), $$ with $p>q>0$ and $A$, $B$, $K$ positive coefficients, is considered. For both $p>q>1$ and $p>1$, $q=1$, we construct stationary solutions, establish their behavior as $|x|\to\infty$ and prove that they are separatrices between solutions decreasing to zero in infinite time and solutions presenting blow-up in finite time. We also establish decay rates for the solutions that decay to zero as $t\to\infty$. |
| title | Qualitative properties of solutions to a generalized Fisher-KPP equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.12900 |