호남수학학술지 (Honam Mathematical Journal)

  • 제17권1호
  • /
  • Pages.107-118
  • /
  • 1995
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

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)
  • 투고 : 1995.05.04
  • 발행 : 1995.07.30
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초록

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 $q^*=max\{q,(N+1)/N\}$.

키워드

과제정보

연구 과제 주관 기관 : Nondirect Research Fund, Korea Research Foundation----

참고문헌

  1. Regional Conference Series in Mathematics v.74 Weak Convergence Methods for Nonlinear Partial Differential Equations, Conference board of the mathematical sciences Evans, L.C.
  2. Maximum principles in differenctial equations Protter, M.H.;Weinberger, H.F.
  3. Reserarch notes in Mathematics v.39 Compensated compactness and applications to partial differential equations Tartar, L.
  4. Singular solutions of semilinear parabolic equations in several space dimensions, Preprint series in GARC-SNU 94-36 Baek, J.S.;Kwak, M.
  5. Jour. of Functional Analysis v.100 Large time behavior for convection diffusion equations in $R^N$ Escobedo, M.;Zuazua, E.
  6. Indiana Univ. Math. Jour. v.42 no.4 A diffusion-convection equation in several space dimensions Escobedo, M.;Vazquez, J.L.;Zuazua, E.
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  8. Duke Math. Jour. v.58 no.3 Classification of singular solutions of a nonlinear heat equation Kamin, S.;Peletier, L.A.;Vazquez, J.L.