Radial Symmetry of Overdetermined Boundary-Value Problems in Exterior Domains

1998 ◽  
Vol 143 (2) ◽  
pp. 195-206 ◽  
Author(s):  
Amandine Aftalion ◽  
Jérôme Busca
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Radial Symmetry ◽  
Exterior Domains

A general blow-up result on nonlinear boundary-value problems on exterior domains

2001 ◽  
Vol 131 (2) ◽  
pp. 451-475 ◽  
Author(s):  
Qi S. Zhang
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Boundary Value ◽  
Porous Medium Equation ◽  
Exterior Domains ◽  
Nonlinear Boundary Value Problems ◽  
Semilinear Equations ◽  
Medium Equation ◽  
Inhomogeneous Porous Medium

In the first part, we study several exterior boundary-value problems covering three types of semilinear equations: elliptic, parabolic and hyperbolic. By a unified approach, we show that these problems share a common critical behaviour. In the second part we prove a blow-up result for an inhomogeneous porous medium equation with the critical exponent, which was left open in a previous paper.

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