Geodesic
Existence and non-existence of global solutions for a semilinear heat equation on a general domain
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 35K58, 35B33, 35B44
Keywords: parabolic equation, blow up, global solution 
@article{EJDE_2014__2014__a61,
     author = {Loayza, Miguel and Da Paix\~ao, Crislene S.},
     title = {Existence and non-existence of global solutions for a semilinear heat equation on a general domain},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a61/}
}
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Loayza, Miguel; Da Paixão, Crislene S. Existence and non-existence of global solutions for a semilinear heat equation on a general domain. Electronic Journal of Differential Equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a61/