NONLOCAL PROBLEM WITH DYNAMICAL BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION

Analytic solutions for the Stephen's inverse problem with local boundary conditions including Elliptic and hyperbolic equations

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

A Well-Posed Free Boundary Value Problem for a Hyperbolic Equation with Dirichlet Boundary Conditions

We construct solutions of a free boundary value problem for a hyperbolic equation with Dirichlet boundary data. This problem arises from a model of deformation of granular media.

Mixed Problem with Nonlocal Boundary Conditions for a Third-order Partial Differential Equation of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem. 2000 Mathematics Subject Classification. 35B45, 35K20, 35M10.

On a nonlocal problem with integral boundary conditions for a multidimensional elliptic equation

A mixed problem with only integral boundary conditions for a hyperbolic equation

We investigate an initial boundary value problem for a second-order hyperbolic equation with only integral conditions. We show the existence, uniqueness, and continuous dependence of a strongly generalized solution. The proof is based on an energy inequality established in a nonclassical function space, and on the density of the range of the operator associated to the abstract formulation of th...