Mixed problem with boundary integral conditions for a certain parabolic 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...

A Boundary Integral Equation with the Generalized Neumann Kernel for a Certain Class of Mixed Boundary Value Problem

1 Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia 2 Department of Mathematics, Faculty of Science, Ibb University, P.O. Box 70270, Ibb, Yemen 3 Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 4 Ibnu Sina Institute for Fundamental Science Studies, Universiti Tek...

On the Boundary Integral Equation Method for a Mixed Boundary Value Problem of the Biharmonic Equation

This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

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.

Mixed Problem with Integral Conditions for a Certain Class of Hyperbolic Equations