相关论文: The Ostrovsky Hunter equation with a space depende…

We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…

We study here the approximation by a finite-volume scheme of a heat equation forced by a Lipschitz continuous multiplicative noise in the sense of It\^o. More precisely, we consider a discretization which is semi-implicit in time and a…

Using the stochastic thermodynamics, we determine the entropy production and the dynamic heat capacity of systems subject to a sinusoidally time dependent temperature, in which case the systems are permanently out of thermodynamic…

Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…

We deal with the Cauchy problem for multi-dimensional scalar conservation laws, where the fluxes and the source terms can be discontinuous functions of the unknown. The main novelty of the paper is the introduction of a~kinetic formulation…

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence and uniqueness of finite time solutions is proved by an extension of the Ovsyannikov method. This result is applied to a…

We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing…

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…

The focus of the present research is on the analysis of local energy stability of high-order (including split-form) summation-by-parts methods, with e.g. two-point entropy-conserving fluxes, approximating non-linear conservation laws. Our…

We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely…

Aerodynamic drag can be partially approximated by the entropy flux across fluid domain boundaries with a formula due to Oswatitsch. In this paper, we build the adjoint solution that corresponds to this representation of the drag and…

In this paper hyperbolic partial differential equations with random coefficients are discussed. We consider the challenging problem of flux functions with coefficients modeled by spatiotemporal random fields. Those fields are given by…

We present the basic equations for stationary, incompressible resistive MHD flows in two dimensions. This leads to a system of differential equations for two flux functions, one elliptic partial differential equation (Grad-Shafranov-like)…

We study the approximation by a semi-discrete finite-volume scheme of the Gross-Pitaevskii equation with time-dependent potential in two dimensions, performing a two-point flux approximation scheme in space. We rigorously analyze the error…

In this article, we propose a novel front tracking scheme for scalar conservation laws with spatially heterogeneous, uniformly convex flux and prove that approximations converge to the unique entropy solution. The main tools are Dafermos'…

In this work we consider a simple, approximate, tending toward exact, solution of the system of two usual Lotka-Volterra differential equations. Given solution is obtained by an iterative method. In any finite approximation order of this…

This paper gives the existence and uniqueness results for solution of fractional differential equations with Hilfer derivative. Using some new techniques and generalizing the restrictive conditions imposed on considered function, the…

We investigate the necessary conditions for the two spacetimes, which are solutions to the Einstein field equations with an anisotropic matter source, to be related to each other by means of a conformal transformation. As a result, we…

A stochastic differential equation with coefficients defined in a scale of Hilbert spaces is considered. The existence, uniqueness and path-continuity of infinite-time solutions is proved by an extension of the Ovsyannikov method. This…

This article concerns a scalar multidimensional conservation law where the flux is of Panov type and may contain spatial discontinuities. We define a notion of entropy solution and prove that entropy solutions are unique. We propose a…