Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ASYMPTOTIC BEHAVIOR OF SINGULAR SOLUTIONS OF SEMILINEAR PARABOLIC EQUATIONS

  • BAN, HYUN JU (Dept. of Mathematics, Chonnam National University) ;
  • KWAK, MINKYU (Dept. of Mathematics, Chonnam National University)
  • Received : 1995.05.04
  • Published : 1995.07.30

Abstract

We study the asymptotic behavior of nonnegative singular solutions of semilinear parabolic equations of the type $$u_t={\Delta}u-(u^q)_y-u^p$$ defined in the whole space $x=(x,y){\in}R^{N-1}{\times}R$ for t>0, with initial data a Dirac mass, ${\delta}(x)$. The exponents q, p satisfy $$1 where $q^*=max\{q,(N+1)/N\}$.

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Acknowledgement

Supported by : Nondirect Research Fund, Korea Research Foundation----

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