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Zbl 0729.35017
Fila, M.; Filo, J.
Blow up for a nonlinear degenerate parabolic equation. (English)
[A] Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 163-166 (1990).

[For the entire collection see Zbl 0704.00019.] \par The paper is a review of some of the authors' previous results concerning both nonlinear degenerate parabolic equations of the type $$ u\sb t=\Delta u\sp m+u\sp p-au,\quad x\in \Omega,\quad t>0\quad (0<m<\infty,\quad p>\max \{1,m\},\quad a\ge 0) $$ with homogeneous Dirichlet boundary data and the heat equation $u\sb t=\Delta u$, $x\in \Omega$, $t>0$ endowed with the nonlinear boundary condition $\partial u/\partial \nu =u\sp p-au$, $x\in \partial \Omega$, $t>0.$ \par Phenomena like blow up in finite or infinite time and the behaviour of $\int\sb{\Omega}\vert u(x,t;u\sb 0)\vert\sp q dx$ for $q>0$ near $t\sb{\max}$ are discussed.
[M.Fila]

MSC 2000:: *35B40 Asymptotic behavior of solutions of PDE
35K60 (Nonlinear) BVP for (non)linear parabolic equations
35K65 Parabolic equations of degenerate type

Keywords: nonlinear degenerate parabolic; heat equation; blow up

Citations: Zbl 0704.00019

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