Stochastic averaging lemmas for kinetic equations
نویسندگان
چکیده
منابع مشابه
Averaging Lemmas and Dispersion Estimates for kinetic equations
Averaging lemmas consist in a regularizing effect on the average of the solution to a linear kinetic equation. Some of the main results are reviewed and their proofs presented in as self contained a way as possible. The use of kinetic formulations for the well posedness of scalar conservation laws is eventually explained as an example of application.
متن کاملRegularity in kinetic formulations via averaging lemmas
We present a new class of averaging lemmas directly motivated by the question of regularity for different nonlinear equations or variational problems which admit a kinetic formulation. In particular they improve the known regularity for systems like γ = 3 in isentropic gas dynamics or in some variational problems arising in thin micromagnetic films. They also allow to obtain directly the best k...
متن کاملA Real Space Method for Averaging Lemmas
We introduce a new method to prove averaging lemmas, i.e. prove a regularizing effect on the average in velocity of a solution to a kinetic equation. The method does not require the use of Fourier transform and the whole procedure is performed in the ’real space’. We are consequently able to improve the known result when the integrability of the solution (or the right hand side of the equation)...
متن کاملOn the Optimality of Velocity Averaging Lemmas
– Studying weak solutions of Burgers’ equation with finite entropy dissipation we show the sharpness of recent results of Jabin and Perthame on velocity averaging. Similar arguments give bounds on the regularity of asymptotic finite-energy states for some variational problems of Ginzburg–Landau type. 2003 Éditions scientifiques et médicales Elsevier SAS RÉSUMÉ. – Nous construisons des solutio...
متن کاملKinetic Semidiscretization of Scalar Conservation Laws and Convergence by Using Averaging Lemmas∗
We consider a time discrete kinetic scheme (known as “transport collapse method”) for the inviscid Burgers equation ∂tu+ ∂x u 2 = 0. We prove the convergence of the scheme by using averaging lemmas without bounded variation estimate. Then, the extension of this result to the kinetic model of Brenier and Corrias is discussed.
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: Séminaire Laurent Schwartz — EDP et applications
سال: 2014
ISSN: 2266-0607
DOI: 10.5802/slsedp.21