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arXiv · 2210.02920

Eternal solutions in exponential self-similar form for a quasilinear reaction-diffusion equation with critical singular potential

Razvan Gabriel Iagar·Marta Latorre·Ariel Sánchez
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Abstract

We prove existence and uniqueness of self-similar solutions with exponential form $$ u(x,t)=e^{\alpha t}f(|x|e^{-\beta t}), \qquad \alpha, \ \beta>0 $$ to the following quasilinear reaction-diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed for $(x,t)\in\real^N\times(0,T)$, with $m>1$, $1 0$ if $u_0$ is compactly supported.

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Razvan Gabriel Iagar, Marta Latorre, Ariel Sánchez. 2022-10-06. Eternal solutions in exponential self-similar form for a quasilinear reaction-diffusion equation with critical singular potential. https://arxiv.org/abs/2210.02920

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