In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, w...

In the analysis of boundary value problems in the theory of plasticity, the general situation arises that different partial differential equations are to be satisfied depending on whether the material is in the plastic or elastic state. The criterion determining the state at any material point depends on the dependent variables and their derivatives with respect to time. Thus the regions of app...

We consider systems governed by a nonlinear parabolic equation, with a distributed control and a disturbance in the initial condition. We prove the existence of solutions to a corresponding minimax problem, and we obtain necessary optimality conditions in the form of Pontryagin’s principles.

In this paper we present a comprehensive existence theory for linear and nonlinear reaction random walk systems. The methods are based on semigroup theory for solutions of differential equations on Banach spaces. The solution properties on a bounded domain sensitively depend on the choice of boundary conditions. For Neumann or for periodic boundary conditions, singularities are transported alon...

We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of arbitrary order, posed on the domain {t > 0, 0 < x < L}. We first show that by analysing the so-called global relation, which is an algebraic relation defined in the complex k-plane coupling all boundary values of the solution, it is possible to ident...

Overview and preliminaries. The study of interacting particle systems with conservation laws frequently revolves around hydrodynamic limits, in which the long-time, large-length scale behavior of a system is characterized by the evolution of the local density of the conserved quantity according to a partial differential equation. The typical setup consists of a particle system defined on a clos...

We consider the problem of approximating a multiple-input multiple-output (MIMO) p×m rational transfer function H(s) of high degree by another p×m rational transfer function b H(s) of much smaller degree, so that the H2 norm of the approximation error is minimized. We characterize the stationary points of the H2 norm of the approximation error by tangential interpolation conditions and also ext...

A Cauchy-characteristic initial value problem for the Einstein-Klein-Gordon system with spherical symmetry is presented. Initial data are specified on the union of a spacelike and null hypersurface. The development of the data is obtained with the combination of a constrained Cauchy evolution in the interior domain and a characteristic evolution in the exterior, asymptotically flat region. The ...

*Correspondence: [email protected] 1Materials Science and Engineering Department, University of California Los Angeles, Los Angeles, California, USA 2Mechanical and Aerospace Engineering Department, University of California Los Angeles, Los Angeles, California, USA Abstract The standard way of modeling plasticity in polycrystals is by using the crystal plasticity model for single crystals in eac...