共查询到20条相似文献,搜索用时 937 毫秒
1.
Hiroyoshi Mitake 《Applied Mathematics and Optimization》2008,58(3):393-410
We study Hamilton-Jacobi equations in a bounded domain with the state constraint boundary condition. We establish a general
convergence result for viscosity solutions of the Cauchy problem for Hamilton-Jacobi equations with the state constraint boundary
condition to asymptotic solutions as time goes to infinity. 相似文献
2.
《Journal of Mathematical Analysis and Applications》1987,125(2):400-450
We study a coupled mathematical system which provides a good model for important families of linear time-invariant hereditary systems: delay-differential equations, integrodifferential equations, Volterra-Stieltjes integral equations, functional differential equations of retarded and neutral types, etc. Appropriate states are constructed and associated semigroups and abstract differential equations are obtained. We emphasize the structural operator approach as in Delfour and Manitius. Control operators are added to the coupled mathematical system allowing delays in the control variables. Again structural operators are introduced to define the state and obtain abstract differential equations without delays in the control variable as in the work of Vinter and Kwong. Finally observation operators are added which allow for delays in the observation variable. Again a new state and a state equations are constructed in such a way that no delay appear in the new observation operator as in the recent work of D. Salamon. 相似文献
3.
4.
We study the local dynamics of one class of nonlinear difference equations which is important for applications. Using perturbation theory methods, we construct sets of singularly perturbed differential-difference equations that are close (in a sense) to initial difference equations. For the problem on the stability of the zero equilibrium state and for certain infinite-dimensional critical cases, we propose a method that allows us to construct analogs of normal forms. We mean special nonlinear boundary value problems without small parameters, whose nonlocal dynamics describes the structure of solutions to initial equations in a small neighborhood of the equilibrium state. We show that dynamic properties of difference and close to them differential-difference equations considerably differ. 相似文献
5.
I. B. Prokopovych 《Journal of Mathematical Sciences》2010,171(4):534-547
We consider the principles of coordinate, rotational, and initial independence of the equations of state for a deformable
material and the theorem on the existence of elasticity potential connected with them. We show that the well-known axiomatic
substantiation and mathematical representation of these principles in “rational continuum mechanics” as well as the proof of the theorem are erroneous. A correct proof of the principles and theorem is presented for the most
general case (a stressed anisotropic body under the action of an arbitrary tensor field) without applying any axioms. On this basis, we eliminated the dependence on an arbitrary initial state and the corresponding
accumulated strain from the system of equations of state of a deformable material. The obtained forms of equations are convenient
for constructing and analyzing the equations of local influence of initial stresses on physical fields of different nature.
Finally, these equations represent governing equations for the problems of nondestructive testing of inhomogeneous three-dimensional
stress fields and for theoretical-and-experimental investigation of the nonlinear equations of state. 相似文献
6.
On Analytical Results for the Optimal Control of the quasi-stationary Radiative Heat Transfer System
Thomas End 《PAMM》2011,11(1):793-794
We state an optimal control problem of the coupled quasi-stationary radiative heat equations consisting of the radiative transfer equation and the instationary heat transfer equation that model radiative-conductive heat transfer. We give an existence and uniqueness result for the state equations and the adjoint equations of the quasi-stationary radiative heat transfer system. For the optimal control problem the existence of a minimizer is proven. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc. 相似文献
8.
We consider a class of nonlinear kinetic Fokker-Planck equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence and convergence rate to the steady state of global classical solution to such kind of equations around the steady state. 相似文献
9.
To solve the boundary-value problem for cylindrical orthotropic shell with sizeable rectangular hole we suggest analytical and numerical method of finite bodies. For determination of the stress state of orthotropic thin-walled cylinder we use a systemof equations that exactly satisfies the equilibrium equations of orthotropic cylindrical shell. Representation of the solutions is divided into basic and self-equilibrium state. For some loads of a shell we build the basic stress state. We obtain a countable number of resolving functions that exactly satisfy the equations of a shell and describe the self-equilibrium stress state. We develop the algorithm of the analytical and numerical solutions of boundary-value problem based on approximation of the stress state of a shell by finite sum of resolving functions and propose a universal way of reduction of all conditions of the contact parts of the enclosure and the boundary conditions to minimize the generalized quadratic forms. We establish criteria under which the construction of approximate solutions coincides with the exact one. 相似文献
10.
We study the problem of consistency of equations of continuum dynamics (using the Euler equations and the continuity equation as examples) and thermodynamic equations of state (for the specific free energy, entropy, and volume). We propose a variant of the Hamiltonian formulation of a model that combines the fluid dynamics of a potential flow of a compressible fluid or gas and local equilibrium thermodynamics into a unified field theory. Thermodynamic equations of state appear in this model as second-class constraint equations. As a consistency condition, there arises another second-class constraint requiring that the product of density and temperature should be independent of time. The model provides an in-principle possibility of finding the time dependence of the specific entropy of the arising dynamical system. 相似文献
11.
A. G. Zagorodny 《Theoretical and Mathematical Physics》2009,160(2):1101-1112
We consider the modern state of a consistent kinetic theory of dusty plasmas. We present the derivation of equations for microscopic
phase densities of plasma particles and grains. Such equations are suitable for extending the Bogoliubov-Born-Green-Kirkwood-Yvon
hierarchy to the case of dusty plasmas and for deriving the kinetic equations with regard for both elastic and inelastic particle
collisions. Moreover, we describe the effective grain-grain potentials kinetically. 相似文献
12.
We consider retarded functional differential equations in the setting of Kurzweil-Henstock integrable functions and we state an averaging result for these equations. Our result generalizes previous ones. 相似文献
13.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(8):951-956
We present, for the BGK equation, asymptotic limits leading to various equations of incompressible and compressible fluid mechanics: the Navier-Stokes equations, the linearized Navier-Stokes equations, the Euler equation, the linearized Euler equation, and the compressible Euler equation. We state a convergence theorem for the nonlinear Navier-Stokes, as well as a result for the linear Navier-Stokes case, and for the compressible Euler equation. 相似文献
14.
We study the boundary control problems for stochastic parabolic equations with Neumann boundary conditions. Imposing super-parabolic conditions, we establish the existence and uniqueness of the solution of state and adjoint equations with non-homogeneous boundary conditions by the Galerkin approximations method. We also find that, in this case, the adjoint equation (BSPDE) has two boundary conditions (one is non-homogeneous, the other is homogeneous). By these results we derive necessary optimality conditions for the control systems under convex state constraints by the convex perturbation method. 相似文献
15.
We study the numerical approximation of Neumann boundary optimal control problems governed by a class of quasilinear elliptic equations. The coefficients of the main part of the operator depend on the state function, as a consequence the state equation is not monotone. We prove that strict local minima of the control problem can be approximated uniformly by local minima of discrete control problems and we also get an estimate of the rate of this convergence. One of the main issues in this study is the error analysis of the discretization of the state and adjoint state equations. Some difficulties arise due to the lack of uniqueness of solution of the discrete equations. The theoretical results are illustrated by numerical tests. 相似文献
16.
C. Tudor 《Mathematische Nachrichten》1990,145(1):135-149
We study the stochastic regulator problem in Hilbert spaces for systems governed by linear stochastic differential equations with retarded controls and with state and control dependent noise. We use integral Riccati equations and no reference to a Riccati differential equation or to the Ito formula is made. 相似文献
17.
Joseph Frédéric Bonnans Constanza Sánchez Fernández de la Vega 《Set-Valued and Variational Analysis》2010,18(3-4):307-326
We consider the optimal control problem of a class of integral equations with initial and final state constraints, as well as running state constraints. We prove Pontryagin’s principle, and study the continuity of the optimal control and of the measure associated with first order state constraints. We also establish the Lipschitz continuity of these two functions of time for problems with only first order state constraints. 相似文献
18.
We study existence and uniqueness of solutions for a general class of second order abstract differential equations with state-dependent delay. Some examples related to partial differential equations with state dependent delay are presented. 相似文献
19.
《Mathematische Nachrichten》2018,291(13):2045-2056
We study the existence and uniqueness of solutions, and the wellposedness of a general class of second order abstract differential equations with state‐dependent delay. Some examples related to partial differential equations with state‐dependent delay are presented. 相似文献
20.
We estimate the rate of convergence to the stationary state for evolution equations which admit many H-theorems with respect to this stationary state. 相似文献