On the Blow-Up Set For Ut = (um)xx m> 1, with Nonlinear Boundary Conditions

M. C. Cortázar (), M. Elgueta () and O. Venegas ()
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M. C. Cortázar: Universidad Católica de Chile, Facultad de Matemáticas
M. Elgueta: Universidad Católica de Chile, Facultad de Matemáticas
O. Venegas: Universidad Católica de Chile, Facultad de Matemáticas

A chapter in Nonlinear Differential Equation Models, 2004, pp 45-56 from Springer

Abstract: Abstract In this paper we give a complete description of the set of blow up points of solutions of the problem $$\begin{gathered} u_t = \left( {u^m } \right)_{xx} {\text{ in }}D_T = [0,\infty ) \times [0,T) \hfill \\ - \left( {u^m } \right)_x \left( {0,t} \right) = u^m \left( {0,t} \right){\text{ on [0,}}T{\text{)}} \hfill \\ u\left( {x,0} \right) = u_0 \left( x \right) \geqslant 0{\text{ on[0, + }}\infty {\text{)}} \hfill \\ \end{gathered} $$ where m> I.

Keywords: Blow-up; porous media (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-7091-0609-9_6

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DOI: 10.1007/978-3-7091-0609-9_6

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