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Certain inverse problems for parabolic equations

Authors:

S. G. Pyatkov

Affiliation:

(1) S. L. Sobolev Institute of Mathematics, Siberian Department of Russian Academy of Sciences, Russia;(2) Yugra State University, Russia

Abstract:

In the paper, we study the inverse problem of finding the solution u and the coefficient q from the following data:

$Mu = u_t - L(x,t,D_x )u + g(x,t,u,nabla u) + q(x,t)u(x,t) = f(x,t), (x,t) in Q = G times (0,T), u/s = varphi (x,t), left. {frac{{partial u}}{{partial n}}} right|_s = psi (x,t), left. u right|_{t = 0} = u_0 (x), S = Gamma times (0,T),$

where G ⊂ ℝⁿ is a bounded domain with boundary Γ and L is a second-order elliptic operator. We prove that the problem is locally solvable in time or in the case where the norms of its data are sufficiently small. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 187–202, 2006.

Keywords:

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