A stability estimate for a solution to the problem of determination of two coefficients of a hyperbolic equation.
A stability estimate for a solution to the wave equation with the Cauchy data on a timelike cylindrical surface.
A steady-state capturing method for hyperbolic systems with geometrical source terms
We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar...
A steady-state capturing method for hyperbolic systems with geometrical source terms
We propose a simple numerical method for capturing the steady state solution of hyperbolic systems with geometrical source terms. We use the interface value, rather than the cell-averages, for the source terms that balance the nonlinear convection at the cell interface, allowing the numerical capturing of the steady state with a formal high order accuracy. This method applies to Godunov or Roe type upwind methods but requires no modification of the Riemann solver. Numerical experiments on scalar...
A study on the budget constrained facility location model considering inventory management cost∗
One of the important issues on the distribution network design is to incorporate inventory management cost into the facility location model. This paper deals with a network model making the decisions on the facility location such as the number of DCs and their locations as well as the decisions on the inventory management such as the ordering quantity and the level of safety stock at each DC. The considered model differs from the previous works by...
A study on the budget constrained facility location model considering inventory management cost∗
One of the important issues on the distribution network design is to incorporate inventory management cost into the facility location model. This paper deals with a network model making the decisions on the facility location such as the number of DCs and their locations as well as the decisions on the inventory management such as the ordering quantity and the level of safety stock at each DC. The considered model differs from the previous works by...
A survey of partial differential equations with piecewise continuous arguments.
A Systematic Approach for Correcting Nonlinear Instabilities. The Lax-Wendroff Scheme for Scalar Conservation Laws.
A THeorem of Global Existence of Solutions to Nonlinear Wave Equations in Four Space Dimensions.
A theory on perturbations of the Dirac operator.
A thermodynamic approach to nonisothermal phase-field models
The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers. As the main result we obtain a general scheme of phase-field models which involves an...
A three-point boundary-value problem for a hyperbolic equation with a non-local condition.
A Transmission Strategy for Hyperbolic Internal Waves of Small Width
Semilinear hyperbolic problems with source terms piecewise smooth and discontinuous across characteristic surfaces yield similarly piecewise smooth solutions. If the discontinuous source is replaced with a smooth transition layer, the discontinuity of the solution is replaced by a smooth internal layer. In this paper we describe how the layer structure of the solution can be computed from the layer structure of the source in the limit of thin layers. The key idea is to use a transmission problem...
A uniformly controllable and implicit scheme for the 1-D wave equation
This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters and . We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order and . Using a discrete...
A uniformly controllable and implicit scheme for the 1-D wave equation
This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters h and Δt. We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order h2 and Δt2. Using...
A unique continuation theorem for the wave equation in the exterior of a characteristic cone
A uniqueness result for the continuity equation in two dimensions
We characterize the autonomous, divergence-free vector fields on the plane such that the Cauchy problem for the continuity equation admits a unique bounded solution (in the weak sense) for every bounded initial datum; the characterization is given in terms of a property of Sard type for the potential associated to . As a corollary we obtain uniqueness under the assumption that the curl of is a measure. This result can be extended to certain non-autonomous vector fields with bounded divergence....
A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.
A wave equation with discontinuous time delay.
A way of estimating the convergence rate of the Fourier method for PDE of hyperbolic type
The Fourier expansion in eigenfunctions of a positive operator is studied with the help of abstract functions of this operator. The rate of convergence is estimated in terms of its eigenvalues, especially for uniform and absolute convergence. Some particular results are obtained for elliptic operators and hyperbolic equations.