کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5778794 1413735 2017 37 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral gap and exponential convergence to equilibrium for a multi-species Landau system
ترجمه فارسی عنوان
شکاف طیفی و همگرایی نمایشی به تعادل برای سیستم چند لاندو
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
In this paper we prove new constructive coercivity estimates and convergence to equilibrium for a spatially non-homogeneous system of Landau equations with moderately soft potentials. We show that the nonlinear collision operator conserves each species' mass, total momentum, total energy and that the Boltzmann entropy is nonincreasing along solutions of the system. The entropy decay vanishes if and only if the Boltzmann distributions of the single species are Maxwellians with the same momentum and energy. A linearization of the collision operator is computed, which has the same conservation properties as its nonlinear counterpart. We show that the linearized system dissipates a quadratic entropy, and prove existence of spectral gap and exponential decay of the solution towards the global equilibrium. As a consequence, convergence of smooth solutions of the nonlinear problem toward the unique global equilibrium is shown, provided the initial data are sufficiently close to the equilibrium. Our proof is based on new spectral gap estimates and uses a strategy similar to [11] based on an hypocoercivity method developed by Mouhot and Neumann in [27].
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 141, Issue 6, August 2017, Pages 509-538
نویسندگان
, ,