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

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Nonlinear Diffusion Equations and Their Equilibrium States, 3

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 7))

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Abstract

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

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Author information

Authors and Affiliations

  1. Math. Institute, University of Oxford, Oxford, OX1 3LB, UK

    Yuan-Wei Qi

Authors
  1. Yuan-Wei Qi
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University College of Wales, Aberystwyth, DYFED SY3BZ, UK

    N. G. Lloyd

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    W. M. Ni  & J. Serrin  & 

  3. Mathematical Institute, Leiden University, PB 9512, 2300 RA, Leiden, The Netherlands

    L. A. Peletier

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© 1992 Springer Science+Business Media New York

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Qi, YW. (1992). The Existence and Asymptotic Behaviour of Similarity Solutions to a Quasilinear Parabolic Equation. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_31

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  • DOI: https://doi.org/10.1007/978-1-4612-0393-3_31

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6741-6

  • Online ISBN: 978-1-4612-0393-3

  • eBook Packages: Springer Book Archive

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