A priori estimates of solutions of superlinear problems

A Priori Estimates of Solutions of Superlinear Problems

In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.

Liouville Theorems, a Priori Estimates, and Blow-up Rates for Solutions of Indefinite Superlinear Parabolic Problems

In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.

A Priori Estimates for Fluid Interface Problems

We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in H 3 2 k+1 and the velocity fields in H 3 2 . These estimates are obtained using geometric considerations which show that the Kelvin-Helmholtz instabilities are a consequence of a curvature calculation.

Optimal a priori estimates for interface problems

A Priori Estimates for Solutions of a Nonlinear Dispersive Equation

In this work we obtain some a priori estimates for a higher order Schrödinger equation and in particular we obtain some a priori estimates for the modified Korteweg-de Vries equation.