Blow-up of sign-changing solutions to quasilinear parabolic equations

Abstract

We study the blow-up of sign-changing solutions to the Cauchy problem for quasilinear parabolic equations of arbitrary order. Our approach is based on H. Levine’s remarkable idea of constructing a concavity inequality for a negative power of a standard positive definite functional. Combining this with the nonlinear capacity method, which is based on the choice of optimal test functions, we find conditions for the blow-up of solutions to the problems under consideration.