@unpublished{ShlapunovTarkhanov2017, author = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Golusin-Krylov Formulas in Complex Analysis}, series = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, volume = {6}, journal = {Preprints des Instituts f{\"u}r Mathematik der Universit{\"a}t Potsdam}, number = {2}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102774}, pages = {25}, year = {2017}, abstract = {This is a brief survey of a constructive technique of analytic continuation related to an explicit integral formula of Golusin and Krylov (1933). It goes far beyond complex analysis and applies to the Cauchy problem for elliptic partial differential equations as well. As started in the classical papers, the technique is elaborated in generalised Hardy spaces also called Hardy-Smirnov spaces.}, language = {en} } @unpublished{MakhmudovMakhmudovTarkhanov2015, author = {Makhmudov, K. O. and Makhmudov, O. I. and Tarkhanov, Nikolai Nikolaevich}, title = {A nonstandard Cauchy problem for the heat equation}, volume = {4}, number = {11}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-83830}, pages = {14}, year = {2015}, abstract = {We consider a Cauchy problem for the heat equation in a cylinder X x (0,T) over a domain X in the n-dimensional space 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on the configuration of S we derive an explicit formula for solutions of this problem.}, language = {en} } @unpublished{DeXingHui2003, author = {De-Xing, Kong and Hui, Yao}, title = {Global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws II}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26565}, year = {2003}, abstract = {In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate fields. It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C¹ functions. In particular, the authors give the optimal control time of the system. Finally, a new application is also given.}, language = {en} } @unpublished{Alsaedy2016, author = {Alsaedy, Ammar}, title = {Variational primitive of a differential form}, volume = {5}, number = {4}, publisher = {Universit{\"a}tsverlag Potsdam}, address = {Potsdam}, issn = {2193-6943}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-89223}, pages = {8}, year = {2016}, abstract = {In this paper we specify the Dirichlet to Neumann operator related to the Cauchy problem for the gradient operator with data on a part of the boundary. To this end, we consider a nonlinear relaxation of this problem which is a mixed boundary problem of Zaremba type for the p-Laplace equation.}, language = {en} }