Electron. J. Diff. Equ., Vol. 2014 (2014), No. 168, pp. 1-9.

Existence and non-existence of global solutions for a semilinear heat equation on a general domain

Miguel Loayza, Crislene S. da Paixao

Abstract:
We consider the parabolic problem $u_t-\Delta u=h(t) f(u)$ in $\Omega \times (0,T)$ with a Dirichlet condition on the boundary and $f, h \in C[0,\infty)$. The initial data is assumed in the space $\{ u_0 \in C_0(\Omega); u_0\geq 0\}$, where $\Omega$ is a either bounded or unbounded domain. We find conditions that guarantee the global existence (or the blow up in finite time) of nonnegative solutions.

Submitted May 27, 2014. Published July 31, 2014.
Math Subject Classifications: 35K58, 35B33, 35B44.
Key Words: Parabolic equation; blow up; global solution.

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Miguel Loayza
Departamento de Matemática
Universidade Federal de Pernambuco - UFPE
50740-540, Recife, PE, Brazil
email: miguel@dmat.ufpe.br
Crislene S. da Paixão
Departamento de Matemática
Universidade Federal de Pernambuco - UFPE
50740-540, Recife, PE, Brazil
email: crisspx@gmail.com

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