A singular solution with smooth initial data for a semilinear parabolic equation
2011
Abstract We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux–Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data.
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