Periodic behavior of solutions to parabolic-elliptic free boundary problems

Viscosity solutions for elliptic-parabolic problems

We study an elliptic-parabolic problem appearing in the theory of partially saturated flows in the framework of viscosity solutions. This is part of current investigation to understand the theory of viscosity solutions for PDE problems involving free boundaries. We prove that the problem is well posed in the viscosity setting and compare the results with the weak theory. Dirichlet or Neumann bo...

Boundary Behavior of Solutions of Parabolic Equations

A boundary backward Harnack inequality is proved for positive solutions of second order parabolic equations in non-divergence form in a bounded cylinder Q = (0; T) which vanish on @ x Q = @ (0; T) ; where is a bounded Lipschitz domain in R n. This inequality is applied to the proof of the HH older continuity of the quotient of two positive solutions vanishing on a portion of @ x Q: 1. Introduct...

Asymptotic analysis of solutions to elliptic and parabolic problems

In the thesis we consider two types of problems. In Paper 1, we study small solutions to a time-independent nonlinear elliptic partial differential equation of Emden-Fowler type in a semi-infinite cylinder. The asymptotic behaviour of these solutions at infinity is determined. First, the equation under the Neumann boundary condition is studied. We show that any solution small enough either vani...

Variational Modeling of Parabolic Free Boundary Problems

Boundary Behavior of Solutions to Second Order Parabolic Equations

1. Introduction In this paper we study some properties of solutions to second order parabolic equations. We consider both divergence (D) and non-divergence (ND) operators L: