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Blow-up at the boundary for degenerate semilinear parabolic equations

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Abstract

This paper treats a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover, it is proved that for a large class of initial data, blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The mathematical analysis is then extended to equations with other degeneracies.

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Authors and Affiliations

  1. Senter for Industriforskning, Blindern, Postboks 124, 0314, Oslo 1, Norway

    M. S. Floater

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  1. M. S. Floater
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Communicated by J. B. McLeod

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Floater, M.S. Blow-up at the boundary for degenerate semilinear parabolic equations. Arch. Rational Mech. Anal. 114, 57–77 (1991). https://doi.org/10.1007/BF00375685

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  • DOI: https://doi.org/10.1007/BF00375685

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