Kinetic Solutions for Nonlocal Stochastic Conservation Laws
نویسندگان
چکیده
This work is devoted to examining the uniqueness and existence of kinetic solutions for a class scalar conservation laws involving nonlocal super-critical diffusion operator multiplicative noise. Our proof based upon analysis on double variables method enabled by parabolic approximation.
منابع مشابه
Nonlocal conservation laws for supersymmetric KdV equations
The nonlocal conservation laws for the N=1 supersymmetric KdV equation are shown to be related in a simple way to powers of the fourth root of its Lax operator. This provides a direct link between the supersymmetry invariance and the existence of nonlocal conservation laws. It is also shown that nonlocal conservation laws exist for the two integrable N=2 supersymmetric KdV equations whose recur...
متن کاملVariational properties of the kinetic solutions of scalar conservation laws
We consider the variational kinetic formulation of the Cauchy problem for a scalar conservation law due to Brenier[] and Panov[]. The solutions in this formulation are represented by a kinetic density function Y that solves a certain differential inclusion ∂tY ∈ A(Y ), in a suitable Hilbert space. In this paper we establish a sufficient “nondegeneracy” condition under which the operator A is th...
متن کاملMultidimensional partial differential equation systems: Nonlocal symmetries, nonlocal conservation laws, exact solutions
For systems of partial differential equations PDEs with n 3 independent variables, construction of nonlocally related PDE systems is substantially more complicated than is the situation for PDE systems with two independent variables. In particular, in the multidimensional situation, nonlocally related PDE systems can arise as nonlocally related subsystems as well as potential systems that follo...
متن کاملStochastic Conservation Laws?
We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created uctuationally from a background Zero Point Field. We conclude that these conservation laws are to be taken in the spirit of thermodynamic laws. Conservation Laws, as is universally known, play an important rol...
متن کاملNonlocal symmetries and nonlocal conservation laws of Maxwell’s equations
Nonlocal symmetries are obtained for Maxwell’s equations in three space–time dimensions through the use of two potential systems involving scalar and vector potentials for the electromagnetic field. Corresponding nonlocal conservation laws are derived from these symmetries. The conservation laws yield nine functionally independent constants of motion which cannot be expressed in terms of the co...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fractional Calculus and Applied Analysis
سال: 2021
ISSN: ['1311-0454', '1314-2224']
DOI: https://doi.org/10.1515/fca-2021-0025