Determination of a time-dependent heat source under not strengthened regular boundary and integral overdetermination conditions

We investigate an inverse problem of finding a time-dependent heat source in a parabolic equation with nonlocal boundary and integral overdetermination conditions. The boundary conditions of this problem are regular but not strengthened regular. The principal difference of this problem is: the system of eigenfunctions is not complete. But the system of eigen- and associated functions forming a basis. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method.

INVERSE PROBLEM WITH INTEGRAL OVERDETERMINATION CONDITION FOR A HYPERBOLIC EQUATION

In the paper, we study an inverse problem for a hyperbolic equation with integral overdetermination condition. The existence of a generalized solution is proved.

Determination of a diffusion coefficient in a quasilinear parabolic equation

This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.