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)
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__a161,
     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},
     year = {2014},
     volume = {2014},
     zbl = {1297.35115},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a161/}
}
TY  - JOUR
AU  - Loayza,  Miguel
AU  - Da Paixão,  Crislene S.
TI  - Existence and non-existence of global solutions for a semilinear heat equation on a general domain
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a161/
LA  - en
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%0 Journal Article
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%A Da Paixão,  Crislene S.
%T Existence and non-existence of global solutions for a semilinear heat equation on a general domain
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a161/
%G en
%F EJDE_2014__2014__a161
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__a161/