We investigate coupled stochastic differential equations governing N nonnegative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires a set of fluctuating variables to be nonnegative and (if appropriately normalized) sum to one. As a result, any stochastic differential equation model to be realizable must not produce events outside of ...

This paper is concerned with the hyperbolic conservation law M i\ Sxa . db(u) _ St + ^ x ^ ~ ° (1.2) u(x,O) = f (x) . By means of the Crandall-Liggett theory of nonlinear semigroups ([1]), it will be shown that the operator A : u H-> ——b(u) Q. X generates a semigroup S = {Sfc; t ;> 0} of contraction operators on L (IR). The function t h-» S.f may then be thought of as a generalized solution of ...

In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes which are the discretization of regular surfaces under consideration. Most import...

The goal of this paper is to calculate of order reduction of the KdV typeequation and the non-isospectral KdV type equation using the μ-symmetrymethod. Moreover we obtain μ-conservation law of the non-isospectral KdVtype equation using the variational problem method.

The use of the symbolic software package GeM for Maple is illustrated with examples of computation of nonlocal symmetries and nonlocal conservation laws of nonlinear partial differential equations. In the considered examples, the nonlocal symmetries and conservation laws arise as local symmetries and conservation laws of potential systems. FullMaple codewith detailed comments is presented. Exam...

Abstract—In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem ...

We present a recently developed Maple-based “GeM” software package for automated symmetry and conservation law analysis of systems of partial and ordinary differential equations (DE). The package contains a collection of powerful easyto-use routines for mathematicians and applied researchers. A standard program that employs “GeM” routines for symmetry, adjoint symmetry or conservation law analy...

The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of the lineari...

Heisenberg’s uncertainty principle, exemplified by the γ ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement contradicts the limit of the accuracy of measurements under conservation laws originally found by Wigner in 1950s, and should be modified to correctly derive the u...

In this paper, we propose to write a source term in the divergence form. A conservation law with a source term can then be written as a single divergence form. We demonstrate that it enables to discretize both the conservation law and the source term in the same framework, and thus greatly simplifies the construction of numerical schemes. To illustrate the advantage of the divergence formulatio...