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CATEGORIES:Mathematics Colloquium
SUMMARY:A characterisation of local existence for semiline
ar heat equations in Lebesgue spaces - Professor J
ames Robinson\, University of Warwick
DTSTART:20161123T160000Z
DTEND:20161123T170000Z
UID:TALK2313AT
URL:/talk/index/2313
DESCRIPTION:joint work with Robert Laister (University of the
West of England)\, Mikolaj Sierzega (Warwick)\, an
d Alejandro Vidal-Lopez (Xi'an Jiaotong-Liverpool
University)\n\nWe consider the nonlinear heat equa
tion $u_t-\\Delta u=f(u)$ with $u(0)=u_0$\, with D
irichlet 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 t
he equation has a local solution bounded in $L^q(\
\Omega)$ for all initial data in $L^q(\\Omega)$ fo
r all $q\\in[1\,\\infty)$.\n\nVersions of our proo
fs are also valid for the case $\\Omega=\\R^d$.\n
LOCATION:Lecture room A\, Watson building
CONTACT:John
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