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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
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