Electronic Journal of Differential Equations,
Vol. 2014 (2014), No. 168, pp. 1-9.
Title: Existence and non-existence of global solutions for a semilinear heat
equation on a general domain
Authors: Miguel Loayza (Univ. Federal de Pernambuco, Recife, PE, Brazil)
Crislene S. da Paixao (Univ. Federal de Pernambuco, Recife, PE, Brazil)
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.