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In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem. 相似文献
34.
Nikolaos S. PAPAGEORGIOU Nikolaos YANNAKAKIS 《数学学报(英文版)》2005,21(5):977-996
This is the first part of a work on second order nonlinear, nonmonotone evolution inclusions defined in the framework of an evolution triple of spaces and with a multivalued nonlinearity depending on both x(t) and x(t). In this first part we prove existence and relaxation theorems. We consider the case of an usc, convex valued nonlinearity and we show that for this problem the solution set is nonempty and compact in C^1 (T, H). Also we examine the Isc, nonconvex case and again we prove the existence of solutions. In addition we establish the existence of extremal solutions and by strengthening our hypotheses, we show that the extremal solutions are dense in C^1 (T, H) to the solutions of the original convex problem (strong relaxation). An example of a nonlinear hyperbolic optimal control problem is also discussed. 相似文献
35.
通过数值求解一维瞬态受激布里渊散射(SBS)声光耦合波方程,从理论上分析了泵浦激光参数及光学材料参数对SBS过程发生阈值的影响。以SBS过程中建立起来的应力场抗拉(压)强度和散射场的反射率为判据,分析了激光脉宽及作用区域长度对激光超声破坏材料效果的影响,探讨了短脉冲激光(约ns)引起的激光超声对材料的破坏机理;讨论了通过参数配置有效遏制SBS过程激光超声对光学材料的破坏问题。 相似文献
36.
The XYZ model describes the interaction between nuclear probes and an electric field gradient that fluctuates among three orthogonal
directions. The model presents a means to calculate the perturbation function that represents spectra obtained using perturbed
angular correlation spectroscopy. Three analytic approximations of the perturbation function have been developed previously,
and they are evaluated in the present paper in the context of Cd jumping among In-lattice sites in In3La. 相似文献
37.
The paper addresses the problem of a semi-infinite plane crack along the interface between two isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond [1998a. Three-dimensional crack-face weight functions for the semi-infinite interface crack-I: variation of the stress intensity factors due to some small perturbation of the crack front. J. Mech. Phys. Solids 46, 489-511, 1998b. Three-dimensional crack-face weight functions for the semi-infinite interface crack-II: integrodifferential equations on the weight functions and resolution J. Mech. Phys. Solids 46, 513-536] applied the “special” method by Bueckner [1987. Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three space. Int. J. Solids Struct. 23, 57-93] and found the expression of the variation of the stress intensity factors for a wavy crack without solving the complete elasticity problem; their solution is expressed in terms of the physical variables, and it involves five constants whose analytical representation was unknown; on the other hand, the “general” solution to the problem has been recently addressed by Bercial-Velez et al. [2005. High-order asymptotics and perturbation problems for 3D interfacial cracks. J. Mech. Phys. Solids 53, 1128-1162], using a Wiener-Hopf analysis and singular asymptotics near the crack front.The main goal of the present paper is to complete the solution to the problem by providing the connection between the two methods. This is done by constructing an integral representation for Lazarus-Leblond's weight functions and by deriving the closed form representations of Lazarus-Leblond's constants. 相似文献
38.
In this paper,we consider a class of quadratic maximization problems.For a subclass of the problems,we show that the SDP relaxation approach yields an approximation solution with the ratio is dependent on the data of the problem with α being a uniform lower bound.In light of this new bound,we show that the actual worst-case performance ratio of the SDP relaxation approach (with the triangle inequalities added) is at least α δd if every weight is strictly positive,where δd > 0 is a constant depending on the problem dimension and data. 相似文献
39.
D. Sasireka E. Palaniyandi K. Iyakutti 《International journal of quantum chemistry》2004,99(3):142-152
Local lattice relaxation of substitutional donors in silicon investigated using self‐consistent multiple scattering Xα (MSXα) method within the framework of the standard muffin‐tin potential approximation is extended to substitutional donors in germanium and substitutional acceptors in both silicon and germanium. Incorporating the effect of lattice relaxation surrounding the impurity makes the model suitable for both shallow and deep levels. Chemical trends of some aspects of impurity states, such as local lattice relaxation and charge transfer, of the impurities both in silicon and germanium are inferred. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004 相似文献
40.
A transient molecular network model is built to describe the nonlinear viscoelasticity of polymers by considering the effect
of entanglement loss and regeneration on the relaxation of molecular strands. It is an extension of previous network theories.
The experimental data on three thermoplastic polymers (ABS, PVC and PA6) obtained under various loading conditions are used
to test the model. Agreement between the theoretical and experimental curves shows that the suggested model can describe successfully
the relaxation behavior of the thermoplastic polymers under different loading rates by using relatively few relaxation modes.
Thus the micromechanism responsible for strain-rate dependence of relaxation process and the origin of nonlinear viscoelasticity
may be disclosed.
The project supported by the National Natural Science Foundation of China and Doctorial Fund 相似文献