论文标题
随机汉堡 - 赫克斯利方程：全球溶解度，较大的偏差和奇特性
Stochastic Burgers-Huxley Equations: Global Solvability, Large Deviations and Ergodicity
论文作者
论文摘要
在这项工作中，我们考虑了由乘法高斯噪声扰动的随机汉堡 - 赫克斯利方程，并讨论了解决方案的全球溶解性结果和渐近行为。我们通过利用线性和非线性操作员的局部单调性能以及对Minty-Browder技术的本地化版本的随机概括，展示了随机汉堡 - 赫克斯利方程的全球强解决方案的存在。然后，我们讨论了随机汉堡 - 赫克斯利方程对汉堡和赫兹利方程的无关极限。通过考虑噪声是加性高斯的噪声，从时间$ t $ $ t $出口的指数估计得出了随机汉堡 - 赫克斯利方程解决方案的解决方案的指数估计，然后在Freidlin-Wentzell类型的大偏差原则的背景下进行了研究。最后，使用溶液的指数稳定性，我们建立了具有与加性高斯噪声的随机汉堡刺激方程的独特的和强烈混合不变的度量的存在。
In this work, we consider the stochastic Burgers-Huxley equation perturbed by multiplicative Gaussian noise, and discuss about the global solvability results and asymptotic behavior of solutions. We show the existence of a global strong solution of the stochastic Burgers-Huxley equation, by making use of a local monotonicity property of the linear and nonlinear operators and a stochastic generalization of localized version of the Minty-Browder technique. We then discuss about the inviscid limit of the stochastic Burgers-Huxley equation to Burgers as well as Huxley equations. By considering the noise to be additive Gaussian, Exponential estimates for exit from a ball of radius $R$ by time $T$ for solutions of the stochastic Burgers-Huxley equation is derived, and then studied in the context of Freidlin-Wentzell type large deviations principle. Finally, we establish the existence of a unique ergodic and strongly mixing invariant measure for the stochastic Burgers-Huxley equation with additive Gaussian noise, using the exponential stability of solutions.
