A three-point boundary value problem with an integral two-space-variables condition for parabolic equations

Approximate Solutions to Three-Point Boundary Value Problems with Two-Space Integral Condition for Parabolic Equations

and Applied Analysis 3 The inner product of H Ω is defined by 〈u x, t , v x, t 〉H 1 ∑ j 0 [ 1 ∑ i 0 ∂ j i tjxi u 0, 0 ∂ i tjxi v 0, 0 ∫1 0 ∂ j 3 tjx3 u x, 0 ∂ 3 tjx3 v x, 0 dx ]

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

On the Weak Solution of a Three-point Boundary Value Problem for a Class of Parabolic Equations with Energy Specification

This paper deals with weak solution in weighted Sobolev spaces, of three-point boundary value problems which combine Dirichlet and integral conditions, for linear and quasilinear parabolic equations in a domain with curved lateral boundaries. We, firstly, prove the existence, uniqueness, and continuous dependence of the solution for the linear equation. Next, analogous results are established f...

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. ...

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.