We analyze a class of weakly differentiable vector fields F : R → R with the property that F ∈ L∞ and div F is a Radon measure. These fields are called bounded divergencemeasure fields. The primary focus of our investigation is to introduce a suitable notion of the normal trace of any divergence-measure field F over the boundary of an arbitrary set of finite perimeter, which ensures the validit...

A closed-form limit on the input level of the double impulse as a substitute of a near-fault ground motion is derived for the overturning of a rigid block. The rocking vibration of the rigid block is formulated by using the conservation law of angular momentum and the conservation law of mechanical energy. The initial rotational velocity after the first impulse and the rotational velocity after...

in thelight of historical and economic circumstances of 1960s, dominant paradigm in international development law was essentially relayed on economic development. but gradually by international efforts and issuing brountland report, the conception of sustainable development came up in context of international law; the conception that by avoiding of mere consideration of economic development and...

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation conditions for deterministic cellular automata. Conservation condition for PCA can also be written in the form of a current conservation law. For deterministic ...

We prove a convergence result for a shock-capturing streamline diffusion finite element method applied to a time-dependent scalar nonlinear hyperbolic conservation law in two space dimensions. The proof is based on a uniqueness result for measure-valued solutions by DiPerna. We also prove an almost optimal error estimate for a linearized conservation law having a smooth exact solution.

A logical error in the usual derivation of the energy conservation law is analyzed, and a way to avoid the error is presented. In earlier papers [1], [2] we identified a logical error adopted by repetition in textbooks on classical electrodynamics when the laws of conservation of energy and momentum are derived for a system consisting of electromagnetic fields and charged particles. In this pap...

In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two assumptions: that words follow Zipf’s law for word frequencies (a power law dependency between frequency and rank) and Zipf’s law of meaning distribution (a power law...

in this paper, a new implicit nonstandard finite difference scheme for conservation laws, which preserving the property of tvd (total variation diminishing) of the solution, is proposed. this scheme is derived by using nonlocal approximation for nonlinear terms of partial differential equation. schemes preserving the essential physical property of tvd are of great importance in practice. such s...

This paper discusses a connection between scalar convex conservation laws and Pontryagin’s minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law is proposed. For scalar space-independent convex conservation laws such a control problem exists and the minimum value solution of the conservation law is eq...