论文标题
重新审视具有超临界非线性的反应扩散系统
Reaction-diffusion systems with supercritical nonlinearities revisited
论文作者
论文摘要
在非线性满足标准单调性假设的情况下，我们对反应扩散系统的分析特性和长期行为进行了全面研究。我们对超临界案例的主要关注，在这种情况下，非线性未从属方程的线性部分，试图对这种非线性提出尽可能小的额外限制。与次级非线性的标准情况相比，超临界情况下这种系统的性质可能大不相同。我们研究了弱解决方案的全球存在和独特性，各种类型的平滑性能，渐近紧凑性以及全球和指数吸引子的存在。
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity satisfies the standard monotonicity assumption. We pay the main attention to the supercritical case, where the nonlinearity is not subordinated to the linear part of the equation trying to put as small as possible amount of extra restrictions on this nonlinearity. The properties of such systems in the supercritical case may be very different in comparison with the standard case of subordinated nonlinearities. We examine the global existence and uniqueness of weak and strong solutions, various types of smoothing properties, asymptotic compactness and the existence of global and exponential attractors.
