Singular backward self-similar solutions of a semilinear parabolic equation | Zendy

Shota Sato | Zendy; Eiji Yanagida | Zendy

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Singular backward self-similar solutions of a semilinear parabolic equation

Author(s) -

Shota Sato,

Eiji Yanagida

Publication year - 2010

Publication title -

discrete and continuous dynamical systems - s

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.481

H-Index - 34

eISSN - 1937-1632

pISSN - 1937-1179

DOI - 10.3934/dcdss.2011.4.897

Subject(s) - singularity , singular solution , mathematics , mathematical analysis , parabolic partial differential equation , nonlinear system , partial differential equation , regular singular point , differential equation , physics , ordinary differential equation , quantum mechanics

We consider a parabolic partial differential equation with power nonlinearity. Our concern is the existence of a singular solution whose singularity becomes anomalous in finite time. First we study the structure of singular radial solutions for an equation derived by backward self-similar variables. Using this, we obtain a singular backward self-similar solution whose singularity becomes stronger or weaker than that of a singular steady state.

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