## Simultaneous determination of two coefficients of a parabolic equation in the case of nonlocal and integral conditions.(English. Ukrainian original)Zbl 0991.35102

Ukr. Math. J. 53, No. 5, 674-684 (2001); translation from Ukr. Mat. Zh. 53, No. 5, 589-596 (2001).
The authors consider equations of the form $u_t=a(t)u_{xx}+c(t)u+f(x,t),\quad 0<x<h,\;0<t<T,$ with an initial condition, boundary conditions involving $$u(0,t),u(h,t),u_x(0,t)$$, and $$u_x(h,t)$$, and given heat moments $$\int_0^hx^iu(x,t) dx$$, $$i=0,1$$. The problem is to find $$a(t),c(t)$$ and $$u(x,t)$$. Existence and uniqueness theorems are obtained.

### MSC:

 35R30 Inverse problems for PDEs 35K15 Initial value problems for second-order parabolic equations

### Keywords:

existence; uniqueness
Full Text: