TY - INPR A1 - Schulze, Bert-Wolfgang T1 - The structure of operators on manifolds with polyhedral singularities N2 - We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities. T3 - Preprint - (2006) 05 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30099 ER - TY - INPR A1 - Chen, Hua A1 - Wu, Shaohua T1 - On existence of solutions for some hyperbolic-parabolic type chemotaxis systems N2 - In this paper, we discuss the local and global existence of week solutions for some hyperbolic-parabolic systems modelling chemotaxis. T3 - Preprint - (2006) 04 KW - Hyperbolic-parabolic system KW - KS model KW - Chemotaxis Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30082 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 - TY - INPR A1 - Gil, Juan B. A1 - Krainer, Thomas A1 - Mendoza, Gerardo A. T1 - On rays of minimal growth for elliptic cone operators N2 - We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays. T3 - Preprint - (2006) 02 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30064 ER - TY - INPR A1 - Kapanadze, D. A1 - Schulze, Bert-Wolfgang A1 - Seiler, J. T1 - Operators with singular trace conditions on a manifold with edges N2 - We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper ‘singular’ trace, potential and Green operators, which are related to the corresponding operators of positive type in Boutet de Monvel’s calculus for boundary value problems. T3 - Preprint - (2006) 01 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30058 ER - TY - INPR A1 - Tarkhanov, Nikolai Nikolaevich A1 - Vasilevski, Nikolai T1 - Microlocal analysis of the Bochner-Martinelli integral N2 - In order to characterise the C*-algebra generated by the singular Bochner-Martinelli integral over a smooth closed hypersurfaces in Cn, we compute its principal symbol. We show then that the Szegö projection belongs to the strong closure of the algebra generated by the singular Bochner-Martinelli integral. T3 - Preprint - (2005) 25 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30012 ER - TY - INPR A1 - Paneah, B. T1 - On the general theory of the cauchy type functional equations with applications in analysis N2 - Contents: 1 The main notations and definitions. 2 Statement of the problems and main results. 2.1 The case of a Z-configuration. 2.2 The case of a P-configuration. 3 Proofs of Theorems 1-7. 4 Applications. 4.1 Multiplicative Cauchy type functional equation. 4.2 On some integral equations relating to a geometric problem 4.3 On the solvability of boundary problem for hyperbolic differential equations. T3 - Preprint - (2005) 24 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30004 ER - TY - INPR A1 - Krupchyk, K. A1 - Tarkhanov, Nikolai Nikolaevich A1 - Tuomela, J. T1 - Generalised elliptic boundary problems N2 - For elliptic systems of differential equations on a manifold with boundary, we prove the Fredholm property of a class of boundary problems which do not satisfy the Shapiro-Lopatinskii property. We name these boundary problems generalised elliptic, for they preserve the main properties of elliptic boundary problems. Moreover, they reduce to systems of pseudodifferential operators on the boundary which are generalised elliptic in the sense of Saks (1997). T3 - Preprint - (2005) 23 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29994 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 - Glebov, S. G. A1 - Kiselev, O. M. T1 - The forced KdV equation and passage through resonance N2 - We construct a special asymptotic solution for the forced KdV equation. In the frame of the shallow water model this kind of the external driving force is related to the atmospheric disturbance. The perturbation slowly passes through a resonance and it leads to the solution exchange. The detailed asymptotic description of the process is presented. T3 - Preprint - (2005) 21 Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29975 ER -