FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 4, PAGES 187-202

**Certain inverse problems for parabolic equations**

S. G. Pyatkov

Abstract

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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,Ñu) + q(x,t)u(x,t) = f(x,t),

(x,t) Î Q =
G ´ (0,T),

u|_{S} = f(x,t),
(¶u)/(¶n)|_{S} =
y(x,t),
u|_{t=0} = u_{0}(x),
S = G ´
(0,T),
where $G$Ì **R**^{n}
is a bounded domain with boundary $$G and $L$ is a second-order
elliptic operator.
We prove that the problem is solvable locally in time or in the case
where the norms of its data are sufficiently small.

Location: http://mech.math.msu.su/~fpm/eng/k06/k064/k06412h.htm

Last modified: February 17, 2007