Mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator

A Mixed Problem for a Boussinesq Hyperbolic Equation with Integral Condition

A hyperbolic problem wich combines a classical(Dirichlet) and a non-local contraint is considered.The existence and uniqueness of strong solutions are proved,we use a functionnal analysis method based on a priori estimate and on the density of the range of the operator generated by the considered problem. 1.INTRODUCTION The first study of evolution problems with a nonlocal condition the so call...

On Initial Boundary Value Problem with Dirichlet Integral Conditions for a Hyperbolic Equation with the Bessel Operator

We consider a mixed problem with Dirichlet and integral conditions for a second-order hyperbolic equation with the Bessel operator. The existence, uniqueness, and continuous dependence of a strongly generalized solution are proved. The proof is based on an a priori estimate established in weighted Sobolev spaces and on the density of the range of the operator corresponding to the abstract formu...

MIXED BOUNDARY VALUE PROBLEM FOR A QUARTER-PLANE WITH A ROBIN CONDITION

We consider a mixed boundary value problem for a quarter-plane with a Robin condition on one edge. We have developed two procedures, one based on the advanced theory of dual integral equations and the other, in our opinion simpler technique, relying on conformal mapping. Both of the procedures are of interest, because the former may be easier to adapt to other boundary value problems.

solving an inverse problem for a parabolic equation with a nonlocal boundary condition in the reproducing kernel space

on the basis of a reproducing kernel space, an iterative algorithm for solving the inverse problem for heat equation with a nonlocal boundary condition is presented. the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution vn is constructed by truncating the series to n terms. the convergence of vn to the analytical solution is also proved. ...

On Three-point Boundary Value Problem with a Weighted Integral Condition for a Class of Singular Parabolic Equations