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University of Birmingham > Talks@bham > Mathematics Colloquium > A characterisation of local existence for semilinear heat equations in Lebesgue spaces
A characterisation of local existence for semilinear heat equations in Lebesgue spacesAdd to your list(s) Download to your calendar using vCal
If you have a question about this talk, please contact John. joint work with Robert Laister (University of the West of England), Mikolaj Sierzega (Warwick), and Alejandro Vidal-Lopez (Xi’an Jiaotong-Liverpool University) We consider the nonlinear heat equation $u_t-\Delta u=f(u)$ with $u(0)=u_0$, with Dirichlet boundary conditions on a bounded domain $\Omega\subset{\mathbb R}d$. We assume that $f\colon[0,\infty)\to[0,\infty)$ is continuous and non-decreasing. We give a characterisation (an “if and only if” result) of those $f$ for which the equation has a local solution bounded in $Lq(\Omega)$ for all initial data in $Lq(\Omega)$ for all $q\in[1,\infty)$. Versions of our proofs are also valid for the case $\Omega=\Rd$. This talk is part of the Mathematics Colloquium series. This talk is included in these lists:Note that ex-directory lists are not shown. |
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