@article{MakhmudovMakhmudovTarkhanov2017, author = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich}, title = {A nonstandard Cauchy problem for the heat equation}, series = {Mathematical Notes}, volume = {102}, journal = {Mathematical Notes}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0001-4346}, doi = {10.1134/S0001434617070264}, pages = {250 -- 260}, year = {2017}, abstract = {We consider the Cauchy problem for the heat equation in a cylinder C (T) = X 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 x (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.}, language = {en} } @article{MakhmudovTarchanov2017, author = {Makhmudov, O. I. and Tarchanov, Nikolaj Nikolaevič}, title = {The first mixed problem for the nonstationary Lam{\´e} system}, series = {The Rocky Mountain journal of mathematics}, volume = {47}, journal = {The Rocky Mountain journal of mathematics}, number = {8}, publisher = {Rocky Mountain Mathematics Consortium}, address = {Tempe}, issn = {0035-7596}, doi = {10.1216/RMJ-2017-47-8-2731}, pages = {2731 -- 2756}, year = {2017}, abstract = {We find an adequate interpretation of the stationary Lam'{e} operator within the framework of elliptic complexes and study the first mixed problem for the nonstationary Lam'{e} system.}, language = {en} }