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Journal of the Korean Mathematical Society = 대한수학회지 v.47 no.4, 2010년, pp.789 - 804   SCIE SCOPUS
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A VERY SINGULAR SOLUTION OF A DOUBLY DEGENERATE PARABOLIC EQUATION WITH NONLINEAR CONVECTION

Fang, Zhong Bo    (SCHOOL OF MATHEMATICAL SCIENCES OCEAN UNIVERSITY OF CHINA  );
  • 초록

    We here investigate an existence and uniqueness of the nontrivial, nonnegative solution of a nonlinear ordinary differential equation: $$[\mid(w^m)]'\mid^{p-2}(w^m)']'\;+\;{\beta}rw'\;+\;{\alpha}w\;+\;(w^q)'\;=\;0$$ satisfying a specific decay rate: $lim_{r\rightarrow\infty}\;r^{\alpha/\beta}w(r)$ = 0 with <TEX>$\alpha$</TEX> := (p - 1)/[pd-(m+1 0 with $\alpha$ := (p - 1)/[pd-(m+1)(p-1)] and $\beta$ := [q-m(p-1)]/[pd-(m+1)(p-1)]. Here m(p-1) > 1 and m(p - 1) $$u_t\;=\;[\mid(u^m)_x\mid^{p-2}(u^m)_x]_x\;+\;(u^q)x$$ defined on the half line.


  • 주제어

    very singular solution .   existence .   uniqueness .   asymptotic behavior.  

  • 참고문헌 (24)

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