A nonstandard Cauchy problem for the heat equation

Autoren: K. Makhmudov, O. Makhmudov, and N. Tarkhanov (2017)

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.

 

Zeitschrift:
Math. Notes
Verlag:
Springer
Seiten:
250–260
Band:
102

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