کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8899920 1631552 2018 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials
ترجمه فارسی عنوان
بر روی نرخ همگرایی به تعادل برای معادله بولتزمن خطی با پتانسیل نرم
کلمات کلیدی
نابرابری کارکردی، آنتروپی، معادله بولتزمن، پتانسیل های نرم افزاری،
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی
In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad's angular cut-off assumption. This is done by an adaptation of the famous entropy method and its variants, resulting in explicit algebraic, or even stretched exponential, rates of convergence to equilibrium under appropriate assumptions. The novelty in our approach is that it involves functional inequalities relating the entropy to its production rate, which have independent applications to equations with mixed linear and non-linear terms. We also briefly discuss some properties of the equation in the non-cut-off case and conjecture what we believe to be the right rate of convergence in that case.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 462, Issue 1, 1 June 2018, Pages 801-839
نویسندگان
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