In this work, we consider the stochastic generalized Burgers–Huxley equation perturbed by space–time white noise and discuss the global solvability results. We show the existence of a unique global mild solution to such equation using a fixed point method and stopping time arguments. The existence of a local mild solution (up to a stopping time) is proved via contraction mapping principle. Then, establishing a uniform bound for the solution, we show the existence and uniqueness of global mild solution to the stochastic generalized Burgers–Huxley equation. Finally, we discuss the inviscid limit of the stochastic Burgers–Huxley equation to the stochastic Burgers as well as Huxley equations.

在这项工作中，我们考虑了时空白噪声干扰的随机广义Burgers-Huxley方程，并讨论了整体可解性结果。我们使用定点方法和停止时间参数来说明此类方程式的唯一全局温和解的存在。通过收缩映射原理证明了局部温和溶液的存在（直至停止时间）。然后，建立解的统一边界，我们证明了随机广义广义Burgers-Huxley方程的整体温和解的存在性和唯一性。最后，我们讨论了随机Burgers–Huxley方程对随机Burgers以及Huxley方程的无形极限。