Geodesic
Blowup and existence of global solutions to nonlinear parabolic equations with degenerate diffusion
Electronic Journal of Differential Equations, Tome 2013 (2013).

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

Summary: In this article, we consider the degenerate parabolic equation $$ u_t-\hbox{div}(|\nabla u|^{p-2}\nabla u) =\lambda u^m+\mu|\nabla u|^q $$ on a smoothly bounded domain $\Omega\subseteq\mathbb{R}^N\; (N\geq2)$, with homogeneous Dirichlet boundary conditions. The values of $p>2, q,m,\lambda$ and $\mu$ will vary in different circumstances, and the solutions will have different behaviors. Our main goal is to present the sufficient conditions for $L^\infty$ blowup, for gradient blowup, and for the existence of global solutions. A general comparison principle is also established.
Classification : 35A01, 35B44, 35K55, 35K92
Keywords: degenerate parabolic equation, L-infinity blowup, gradient blowup, global solution, comparison principle 
@article{EJDE_2013__2013__a67,
     author = {Zhang, Zhengce and Li, Yan},
     title = {Blowup and existence of global solutions to nonlinear parabolic equations with degenerate diffusion},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2013},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a67/}
}
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Zhang, Zhengce; Li, Yan. Blowup and existence of global solutions to nonlinear parabolic equations with degenerate diffusion. Electronic Journal of Differential Equations, Tome 2013 (2013). http://geodesic.mathdoc.fr/item/EJDE_2013__2013__a67/