Global solvability for quasilinear parabolic equation with inhomogeneous density and a source

Abstract

We study the Cauchy problem for quasilinear parabolic equation with inhomogeneous density and a source. We show that this problem has a global solution under the assumptions that initial datum is small enough in the integral sense and the source term has overcritical behaviour. The sharp estimates of a solution is obtained as well.

Keywords:

• quasilinear parabolic equation
• inhomogeneous density
• Fujita critical exponent
• global existence

AMS Subject Classifications::

• 35B33
• 35B45
• 35K55
• 35K65