We consider a stochastic perturbation of a moving boundary problem proposed by Ludford and Stewart and studied by Caffarelli and Vazquez. We prove existence and uniqueness.

A nonlinear degenerate convection-diffusion initial boundary value problem is studied in a bounded domain. A dynamical boundary condition (containing the time derivative of a solution) is prescribed on the one part of the boundary. This models a non-perfect contact on the boundary. Existence and uniqueness of a weak solution in corresponding function spaces is proved using the backward Euler me...

This paper explores the continuous time and continuous space model of racing under uncertainty put forward by Budd, Harris, and Vickers (1993) and allows for potentially asymmetric players. To prove the existence of Markov perfect equilibria, I use a boundary value problem formulation which is novel to the dynamic competition literature. In addition, by providing a new and intuitive definition ...

The theory of Riemann boundary value problem for analytic functions of one complex variable and singular integral equations that are equivalent to it has been extensively studied in the literature. For classical books on this topic see [7, 12, 13] and for an actual overview of them the reader is directed to the monograph by Estrada and Kanwal [6], and the references therein. In the more recent ...

In this work, we establish sufficient conditions for the existence of solutions for a three point boundary value problem generated by a third order differential equation. We give sufficient conditions that allow us to obtain the existence of a nontrivial solution. Then by using the Leray Schauder nonlinear alternative we prove the existence of at least one solution of the posed problem. As an a...

We use a direct variational method in order to investigate the dependence on parameter for the solution for a Duffing type equation with Dirichlet boundary value conditions. Mathematics Subject Classification. 49J02

Consider a bounded domain G C R (_N>1) with smooth boundary T . Let L be a uniformly elliptic linear differential operator. Let y and ß be two maximal monotone mappings in R. We prove that, when y ? 2 satisfies a certain growth condition, given f £ L (G ) there is u € H (G) such that Lu + y(u) 3 f a.e. on G, and -du/d v e ß(u\ ) a.e. on T, where du/civ is the conormal derivative associated with...

On the basis of generalization of upper and lower solution method to the singular two point boundary value problems, the existence theorem of solutions for the system, which models a process of magnetic insulation in plasma is proved.

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...