Related papers: Statistical solutions of hyperbolic conservation l…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
For discretisations of hyperbolic conservation laws, mimicking properties of operators or solutions at the continuous (differential equation) level discretely has resulted in several successful methods. While well-posedness for nonlinear…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the…
The aim of this paper is to establish time decay properties and dispersive estimates for strictly hyperbolic equations with homogeneous symbols and with time-dependent coefficients whose derivatives are integrable. For this purpose, the…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
In this paper we apply the formalism of translation invariant (continuous) matrix product states in the thermodynamic limit to $(1+1)$ dimensional critical models. Finite bond dimension bounds the entanglement entropy and introduces an…
The entropy conservative/stable algorithm of Friedrich~\etal (2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary…
A general framework for the theory of statistical solutions on trajectory spaces is constructed for a wide range of equations involving incompressible viscous flows. This framework is constructed with a general Hausdorff topological space…
This paper is concerned with the proof of existence and numerical approximation of large-data global-in-time Young measure solutions to initial-boundary-value problems for multidimensional nonlinear parabolic systems of forward-backward…
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…
Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…
For the system of polyconvex adiabatic thermoelasticity, we define a notion of dissipative measure-valued solution, which can be considered as the limit of a viscosity approximation. We embed the system into a symmetrizable hyperbolic one…
We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy…
We propose a family of "exactly solvable" probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free…
We introduce a kinetic formulation for scalar conservation laws with nonlocal and nonlinear diffusion terms. We deal with merely L 1 initial data, general self-adjoint pure jump L{\'e}vy operators, and locally Lipschitz nonlinearities of…
A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a…
The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
This paper deals with diffusive limit of the p-system with damping and its approximation by an Asymptotic Preserving (AP) Finite Volume scheme. Provided the system is endowed with an entropy-entropy flux pair, we give the convergence rate…