Geometric Analysis Seminar
Speaker: Christos Sourdis (National and Kapodistrian University of Athens)
Title: Liouville type theorems for ancient solutions to the equation $u_t=\Delta u+|u|^{p-1}u$ with critical or supercritical exponent.
Abstract: Firstly, we will provide a survey of Liouville type results for global, ancient or eternal solutions to the nonlinear heat equation $u_t=\Delta u+|u|^{p-1}u$, $p>1$, in the whole space. We will then turn our attention to critical or supercritical exponents $p$ with respect to the Sobolev embedding. In that regime, the steady state problem has a continuum of sign-definite radially symmetric solutions, including singular ones, that decay to zero at infinity. We will particularly focus on the case where $p$ is larger or equal to the so called Joseph-Lundgren exponent, in which case the aforementioned radial steady states form a foliation. Our Liouville type results imply the quasiconvergence as $t\to +\infty$ of a class of solutions to the corresponding initial value problem.
Dial-In Information
https://tennessee.zoom.us/j/91228266699
Tuesday, March 23, 2021 at 2:50pm to 4:05pm
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Theodora Bourni
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