Reduced measures associated to parabolic problems

Details Reduced measures associated to parabolic problems Reduced measures associated to parabolic problems

2008-05-27

arxiv.org/abs/0805.4125v1

Proceedings of the Steklov Institute of Mathematics 260 (2008) 3-25

Mathematics

Analysis of PDEs

Scientific paper

We study the existence and the properties of the reduced measures for the parabolic equations $\partial_tu-\Delta u+g(u)=0$ in $\Omega\times (0,\infty)$ subject to the conditions ($P$): $u=0$ on $\partial\Omega\times (0,\infty)$, $u(x,0)=\mu$ and ($P'$): $u=\mu'$ on $\partial\Omega\times (0,\infty)$, $u(x,0)=0$ where $\mu$ and $\mu'$ are positive Radon measures and $g$ a continuous nondecreasing function

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