Michael V. Klibanov and Alexander V. Tikhonravov
Estimates of initial conditions of parabolic equations in via lateral Cauchy data in infinite domains
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ABSTRACT.  A parabolic equation or inequality in an infinite domain is considered. The lateral Cauchy data for this equation are assumed to be given at an arbitrary smooth lateral surface. An inverse problem of the interest of this paper consists in an estimate of the unknown initial condition via these Cauchy data.