Estimates of initial conditions of parabolic equations in via lateral Cauchy data in infinite domains
نویسندگان
چکیده
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.
منابع مشابه
Estimates of Initial Conditions of Parabolic Equations and Inequalities Via the Lateral Cauchy Data
A parabolic equation and, more generally, parabolic inequality is considered in the cylinder QT = Ω × (0, T ) , where Ω ⊂ Rn is a bounded domain. Cauchy data, i.e., both Dirichlet and Neumann data are given at the lateral surface ST = ∂Ω × (0, T ). Logarithmic stability estimates are obtained for the unknown initial condition at {t = 0}. These estimates enable one to establish convergence rate ...
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