Geodesic
Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating
Electronic journal of differential equations, Tome 2002 (2002)
We consider a non-local initial boundary-value problem for the equation

$ u_t=\Delta u+\lambda f(u)/\Big(\int_{\Omega}f(u)\,dx\Big)^2 ,\quad x \in \Omega \subset \mathbb{R}^2 ,\,\;t>0, $

where $u$ represents a temperature and $f$ is a positive and decreasing function. It is shown that for the radially symmetric case, if $u$ blows up, whereas for $\lambda=\lambda^{\ast}$ at least one solution. Stability and blow-up of these solutions are examined in this article.
Classification : 35B30, 35B40, 35K20, 35K55, 35K99
Keywords: nonlocal parabolic equations, blow-up, global existence, steady states 
@article{EJDE_2002__2002__a60,
     author = {Tzanetis,  Dimitrios E.},
     title = {Blow-up of radially symmetric solutions of a non-local problem modelling {Ohmic} heating},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {0993.35018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a60/}
}
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Tzanetis,  Dimitrios E. Blow-up of radially symmetric solutions of a non-local problem modelling Ohmic heating. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a60/