TY - JOUR A1 - Makhmudov, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A nonstandard Cauchy problem for the heat equation JF - Mathematical Notes N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1134/S0001434617070264 SN - 0001-4346 SN - 1573-8876 VL - 102 SP - 250 EP - 260 PB - Pleiades Publ. CY - New York ER - TY - INPR A1 - Makhmudov, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - A nonstandard Cauchy problem for the heat equation N2 - 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. T3 - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015)11 KW - heat equation KW - Cauchy problem KW - Carleman formulas Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-83830 SN - 2193-6943 VL - 4 IS - 11 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. A1 - Tarkhanov, Nikolai Nikolaevich T1 - The cauchy problem of couple-stress elasticity T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2006 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - The cauchy problem for the lame system in infinite domains in Rm T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - BOOK A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - Regularization of the cauchy problem for the system of elasticity theory in Rm T3 - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Y1 - 2005 SN - 1437-739X PB - Univ. CY - Potsdam ER - TY - INPR A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - Regularization of the Cauchy Problem for the System of Elasticity Theory in R up (m) N2 - In this paper we consider the regularization of the Cauchy problem for a system of second order differential equations with constant coefficients. T3 - Preprint - (2005) 22 KW - the Cauchy problem KW - Lame system KW - elliptic system KW - ill-posed problem KW - Carleman matrix KW - regularization KW - Laplace equation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29983 ER - TY - INPR A1 - Makhmudov, O. I. A1 - Niyozov, I. E. T1 - The Cauchy problem for the Lame system in infinite domains in R up(m) N2 - We consider the problem of analytic continuation of the solution of the multidimensional Lame system in infinite domains through known values of the solution and the corresponding strain tensor on a part of the boundary, i.e,the Cauchy problem. T3 - Preprint - (2005) 20 KW - the Cauchy problem KW - system Lame KW - elliptic system KW - illposed problem KW - Carleman matrix KW - regularization KW - Laplace equation Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29967 ER - TY - JOUR A1 - Makhmudo, K. O. A1 - Makhmudov, O. I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - Equations of Maxwell type JF - Journal of mathematical analysis and applications N2 - For an elliptic complex of first order differential operators on a smooth manifold X, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to that of classical Maxwell's equations. The paper focuses on boundary value problems for the abstract Maxwell equations, especially on the Cauchy problem. KW - Electromagnetic waves KW - Scattering KW - Elliptic complex KW - Green formulas KW - Stratton-Chu formulas KW - Cauchy problem Y1 - 2011 U6 - https://doi.org/10.1016/j.jmaa.2011.01.012 SN - 0022-247X VL - 378 IS - 1 SP - 64 EP - 75 PB - Elsevier CY - San Diego ER - TY - JOUR A1 - Makhmudov, O. I. A1 - Tarchanov, Nikolaj Nikolaevič T1 - The first mixed problem for the nonstationary Lamé system JF - The Rocky Mountain journal of mathematics N2 - 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. KW - Lame system KW - evolution equation KW - first boundary value problem Y1 - 2018 U6 - https://doi.org/10.1216/RMJ-2017-47-8-2731 SN - 0035-7596 SN - 1945-3795 VL - 47 IS - 8 SP - 2731 EP - 2756 PB - Rocky Mountain Mathematics Consortium CY - Tempe ER - TY - INPR A1 - Makhmudov, O. A1 - Niyozov, I. A1 - Tarkhanov, Nikolai Nikolaevich T1 - The cauchy problem of couple-stress elasticity N2 - We study the Cauchy problem for the oscillation equation of the couple-stress theory of elasticity in a bounded domain in R3. Both the displacement and stress are given on a part S of the boundary of the domain. This problem is densely solvable while data of compact support in the interior of S fail to belong to the range of the problem. Hence the problem is ill-posed which makes the standard calculi of Fourier integral operators inapplicable. If S is real analytic the Cauchy-Kovalevskaya theorem applies to guarantee the existence of a local solution. We invoke the special structure of the oscillation equation to derive explicit conditions of global solvability and an approximation solution. T3 - Preprint - (2006) 03 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30078 ER -