TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Formal Poincaré lemma
N2  - We show how the multiple application of the formal Cauchy-Kovalevskaya theorem leads to the main result of the formal theory of overdetermined systems of partial differential equations. Namely, any sufficiently regular system Au = f with smooth coefficients on an open set U ⊂ Rn admits a solution in smooth sections of a bundle of formal power series, provided that f satisfies a compatibility condition in U.
T3  - Preprint - (2007) 02 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30231
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Ke
T1  - The existence and regularity of multiple solutions for a class of infinitely degenerate elliptic equations
N2  - Let X = (X1,.....,Xm) be an infinitely degenerate system of vector fields, we study the existence and regularity of multiple solutions of Dirichelt problem for a class of semi-linear infinitely degenerate elliptic operators associated with the sum of square operator Δx = ∑m(j=1) Xj* Xj.
T3  - Preprint - (2007) 03 
KW  - degenerate elliptic equations
KW  - Logarithmic Sobolev inequality
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30247
ER  - 
TY  - INPR
A1  - Yagdjian, Karen
A1  - Galstian, Anahit
T1  - Fundamental solutions for wave equation in de Sitter model of universe
N2  - In this article we construct the fundamental solutions for the wave equation arising in the de Sitter model of the universe. We use the fundamental solutions to represent solutions of the Cauchy problem and to prove the Lp − Lq-decay estimates for the solutions of the equation with and without a source term.
T3  - Preprint - (2007) 06 
KW  - de Sitter model ; Fundamental solutions ; Decay estimates
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30271
ER  - 
TY  - INPR
A1  - Chen, Hua
A1  - Li, Wei-Xi
A1  - Xu, Chao-Jiang
T1  - Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations
N2  - This paper studies the Gevrey regularity of weak solutions of a class of linear and semilinear Fokker-Planck equations.
T3  - Preprint - (2007) 07 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30283
ER  - 
TY  - INPR
A1  - Ly, I.
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - The cauchy problem for nonlinear elliptic equations
N2  - This paper is devoted to investigation of the Cauchy problem for nonlinear elliptic equations with a small parameter.
T3  - Preprint - (2007) 01 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30228
ER  - 
TY  - INPR
A1  - Yin, Yang
A1  - Hua, Chen
T1  - On chemotaxis systems with saturation growth
N2  - In this paper, we discuss the global existence of solutions for Chemotaxis models with saturation growth. If the coe±cients of the equations are all positive smooth T-periodic functions, then the problem has a positive T-periodic solution, and meanwhile we discuss here the stability problems for the T-periodic solutions.
T3  - Preprint - (2007) 04 
KW  - Saturation model
KW  - Chemotaxis
KW  - global solution
KW  - asymptotic stable
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30254
ER  - 
TY  - INPR
A1  - Flad, Heinz-Jürgen
A1  - Schneider, Reinhold
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential
N2  - We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.
T3  - Preprint - (2007) 05 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30268
ER  -