The Cauchy problem for a parabolic equation in the cylinder CT=D × (0,T) over a domain D in space R³ with initial data given on a strip on the lateral surface of the cylinder is considered. The strip has the form S × (0,T) , where S is an open subset of the boundary of D . The problem is ill-posed. Under certain natural constraints on the strip configuration, an explicit formula for the solutions of this problem is obtained.
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Makhmudov et al. (2026) studied this question.
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