Geodesic
Qualitative properties of solutions to semilinear heat equations with singular initial data
Electronic Journal of Differential Equations, Tome 2004 (2004).

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

Summary: This article concerns the nonnegative solutions to the Cauchy problem $$\displaylines{ u_t - \Delta u + b(x,t)|u|^{p-1}u = 0 \quad \hbox{in } \mathbb{R}^N \times (0,{\infty}), \cr u(x,0) = u_0(x) \quad \hbox{in } \mathbb{R}^N \,. }$$ We investigate how the comparison principle, extinction in finite time, instantaneous shrinking of support, and existence of solutions depend on the behaviour of the coefficient $b(x,t)$.
Classification : 35B05, 35K55
Keywords: comparison principle, extinction, shrinking of support, existence 
@article{EJDE_2004__2004__a43,
     author = {Li, Junjie},
     title = {Qualitative properties of solutions to semilinear heat equations with singular initial data},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2004},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a43/}
}
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Li, Junjie. Qualitative properties of solutions to semilinear heat equations with singular initial data. Electronic Journal of Differential Equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a43/