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arXiv · 2411.12900

Qualitative properties of solutions to a generalized Fisher-KPP equation

Razvan Gabriel Iagar·Ariel Sánchez
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Abstract

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 $t\to\infty$.

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Razvan Gabriel Iagar, Ariel Sánchez. 2024-11-19. Qualitative properties of solutions to a generalized Fisher-KPP equation. https://arxiv.org/abs/2411.12900

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