Higher Dimensional Blow Up for Semilinear Parabolic Equations

Abstract

We consider the Cauchy problem where is a continuous, nonnegative and bounded function. It is well known that the solution may blow up in a finite time. We shall be concerned here with the asymptotic behaviour of as blow up is approached. In particular the final profile of near blow up points is studied, and the fact that the blow up set has zero Lebesgue measure is proved.

Keywords:

• Blow up, asymptotic behavior
• semilinear parabolic equations AMS(MOS) subject classifications. 35B40, 35K55, 35K57

Additional information

Notes on contributors

J. J. L. Velázquez