A nonstandard Cauchy problem for the heat equation
K. O. MakhmudovAlisher-Navoi Samarkand State University, Samarkand, UzbekistanО. И. МахмудовAlisher-Navoi Samarkand State University, Samarkand, UzbekistanНиколай ТархановInstitut für Mathematik, Universität Potsdam, Potsdam, Germany
ABI
Аннотация
We consider the Cauchy problem for the heat equation in a cylinder C T = X × (0, T) over a domain X in R n , with data on a strip lying on the lateral surface. The strip is of the form S × (0, T), where S is an open subset of the boundary of X. The problem is ill-posed. Under natural restrictions on the configuration of S, we derive an explicit formula for solutions of this problem.
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