Large Time Behavior of Solutions to Stochastic Partial Differential Equations

我们将研究由随机偏微分方程描述的复杂系统的平衡点。在物理上相关的假设下，将得到由高斯噪声和一般Levy噪声驱动的方程的收敛到平衡的速率。该项目对澳大利亚的好处包括提高其在国际社会中的科学地位，对澳大利亚研究人员进行复杂系统数学分析前沿方法的培训，并与这一研究领域的世界领导人建立密切联系。该项目将促进我们对物理学、工程学、社会科学和生命科学中复杂系统的理解，因此符合优先目标：突破性科学。

We will study equilibria of complex systems described by stochastic partial differential equations. The rates of convergence to equilibrium will be obtained for the equations driven by Gaussian and general Levy noises under physically relevant assumptions. The benefits of this project to the nation include enhancing its scientific standing in the international community, the training of Australian researchers in forefront methods of mathematical analysis of complex systems and development of close ties with the world leaders in this area of research. The project will advance our understanding of complex systems arising in Phyiscs, Engineering, Social and Life Sciences, hence fits into the Priority Goal: Breakthrough Science.