Continuous solutions for a degenerate free boundary problem

Optimal Solutions for a Free Boundary Problem for Crystal Growth

We consider a free boundary problem modeling the growth/dissolution of a crystal in a radially symmetric setting. Existence of an optimal boundary control, minimizing a cost functional of a standardìntegral-quadratic' form, is already known and we here consider the characterization and computation of such an optimal control.

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

A two-phase free boundary problem for a semilinear elliptic equation

In this paper we study a two-phase free boundary problem for a semilinear elliptic equation on a bounded domain $Dsubset mathbb{R}^{n}$ with smooth boundary‎. ‎We give some results on the growth of solutions and characterize the free boundary points in terms of homogeneous harmonic polynomials using a fundamental result of Caffarelli and Friedman regarding the representation of functions whose ...

A Free Boundary Problem for a Quasi-linear Degenerate Elliptic Equation: Regular Reflection of Weak Shocks

We prove the existence of a solution to the weak regular reflection problem for the unsteady transonic small disturbance (UTSD) model for shock reflection by a wedge. In weak regular reflection, the state immediately behind the reflected shock is supersonic and constant. The flow becomes subsonic further downstream; the equation in self-similar coordinates is degenerate at the sonic line. The r...

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation