Singular backward self-similar solutions of a semilinear parabolic equation
Shota Sato - Mathematical Institute, Tohoku University, Sendai 980-8578, Japan (email)
Abstract: 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.
Keywords: Semilinear parabolic equation,
backward self-similar solution, singular solution,
Received: September 2009; Revised: December 2009; Published: November 2010.