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Asymptotic behavior of singular solutions for a semilinear parabolic equation

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  • We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. It is known that in some range of parameters, this equation has a family of singular steady states with ordered structure. Our concern in this paper is the existence of time-dependent singular solutions and their asymptotic behavior. In particular, we prove the convergence of solutions to singular steady states. The method of proofs is based on the analysis of a related linear parabolic equation with a singular coefficient and the comparison principle.
    Mathematics Subject Classification: Primary: 35K58; Secondary: 35B33, 35B35.


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