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Boundary blow-up of a logistic-type porous media equation in a multiply connected domain

Published online by Cambridge University Press:  04 February 2010

Huiling Li ,
Peter Y. H. Pang  and
Mingxin Wang
Huiling Li
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210018, People's Republic of China
Peter Y. H. Pang
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, 117543 Republic of Singapore, ([email protected])
Mingxin Wang
Affiliation:
Department of Mathematics, Southeast University, Nanjing 210018, People's Republic of China and Science Research Center, Harbin Institute of Technology, Harbin 150080, People's Republic of China
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Abstract

We study positive solutions to the porous media equation of degenerate logistic type −Δu = a(x)u1/m – b(x)f(u), m > 1, which blow up at the inner boundary and satisfy a homogeneous boundary condition at the outer boundary of a multiply connected domain. In particular, we investigate uniqueness and blow-up rate near the inner boundary for such solutions. We also look at the limiting behaviour as m ↘ 1 for the special case where b(x) > 0 and f(u) = up/m with p > m.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 1 , February 2010 , pp. 101 - 117
Copyright
Copyright © Royal Society of Edinburgh 2010

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