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Reliable solution of linear parabolic problems with respect to uncertain coefficients. (English) Zbl 0928.35016
Summary: A class of parabolic initial-boundary value problems is considered, where the admissible coefficients are given in certain intervals. We are looking for maximal values of the solution with respect to the set of admissible coefficients. The existence of a maximal solution is proven both in the continuous and in a discretized formulation, where the Rothe’s method and finite elements are employed. Some convergence analysis is also presented.

MSC:
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
49J22 Optimal control problems with integral equations (existence) (MSC2000)
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