The Existence and Asymptotic Behaviour of Similarity Solutions to a Quasilinear Parabolic Equation

  • Yuan-Wei Qi
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)


In this paper we study the existence and properties of similarity solutions which blow-up in finite time, of the nonlinear parabolic equation where 0 < α < 1, p > 1. This is a transformation of the well-known porous media equation which can be regarded as to describe the propagation of thermal perturbations in a medium with a nonlinear heat conduction coefficient and a heat source term, depending on the temperature. Indeed, let v be a solution of porous media equation


Similarity Solution Symmetric Solution Nonlinear Parabolic Equation QUASILINEAR Parabolic Equation Linear Heat Equation 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Yuan-Wei Qi
    • 1
  1. 1.Math. InstituteUniversity of OxfordOxfordUK

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