Estimate of the solution of the Dirichlet problem for parabolic equations and applications

AbstractIn the present paper we consider the Dirichlet problem for quasilinear nonuniformly parabolic equations. A new sufficient condition which guarantees the a priori estimate of the maximum of the modulus of the solution is formulated. A several applications of this estimate are given

Space dimension can prevent the blow-up of solutions for parabolic problems

In the present paper, we investigate the preventive role of space dimension for semilinear parabolic problems. Conditions guaranteeing the absence of the blow-up of the solutions are formulated