Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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LONG-TIME BEHAVIOR FOR SEMILINEAR DEGENERATE PARABOLIC EQUATIONS ON ℝN

  • Cung, The Anh (Department of Mathematics Hanoi National University of Education) ;
  • Le, Thi Thuy (Department of Mathematics Electric Power University)
  • Received : 2012.03.13
  • Published : 2013.10.31
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Abstract

We study the existence and long-time behavior of solutions to the following semilinear degenerate parabolic equation on $\mathbb{R}^N$: $$\frac{{\partial}u}{{\partial}t}-div({\sigma}(x){\nabla}u+{\lambda}u+f(u)=g(x)$$, under a new condition concerning a variable non-negative diffusivity ${\sigma}({\cdot})$. Some essential difficulty caused by the lack of compactness of Sobolev embeddings is overcome here by exploiting the tail-estimates method.

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References

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