论文标题
非线性产生重组模型的低碳率和反应扩散极限
Hypocoercivity and reaction-diffusion limit for a nonlinear generation-recombination model
论文作者
论文摘要
在平坦的圆环上考虑了两种物质气体混合物的反应 - 动作模型。对于具有非移动恒温背景的主要散射，对反应扩散系统的宏观极限进行了。通过低调估计值证明了对平衡的指数衰减。这似乎是从动力学模型中非线性反应 - 扩散系统的第一个严格推导，也是非线性动力学问题的第一个低调结果，而没有小假设。分析从溶液的均匀界限的平衡速度分布中获利。
A reaction-kinetic model for a two-species gas mixture undergoing pair generation and recombination reactions is considered on a flat torus. For dominant scattering with a non-moving constant-temperature background the macroscopic limit to a reaction-diffusion system is carried out. Exponential decay to equilibrium is proven for the kinetic model by hypocoercivity estimates. This seems to be the first rigorous derivation of a nonlinear reaction-diffusion system from a kinetic model as well as the first hypocoercivity result for a nonlinear kinetic problem without smallness assumptions. The analysis profits from uniform bounds of the solution in terms of the equilibrium velocity distribution.
