论文标题
解决随机广义汉堡方程的解决方案的绝对连续性
Absolute continuity of the solution to stochastic generalized Burgers-Huxley equation
论文作者
论文摘要
本工作涉及解决方案定律对随机广义汉堡（SGBH）方程的全局可溶性以及绝对连续性，该方程在$ \ mathbb {r} $的有限间隔内由乘法时空白噪声驱动。我们首先在截断论证和收缩映射原理的帮助下，证明存在独特的局部温和解决方案。然后，通过使用局部温和解决方案的均匀边界和停止时间参数来获得全局可溶性结果。后来，我们建立了一个比较定理，用于具有高阶非线性的SGBH方程解决方案，并且在这项工作中起着至关重要的作用。然后，我们讨论了Malliavin微积分感中SGBH方程的解决方案的弱点。最后，我们在$ \ mathbb {r} $上获得了解决方案定律的绝对连续性，并在比较定理和溶液的弱点的帮助下存在密度。
The present work deals with the global solvability as well as absolute continuity of the law of the solution to stochastic generalized Burgers-Huxley (SGBH) equation driven by multiplicative space-time white noise in a bounded interval of $\mathbb{R}$. We first prove the existence of a unique local mild solution to SGBH equation with the help of a truncation argument and contraction mapping principle. Then global solvability results are obtained by using uniform bounds of the local mild solution and stopping time arguments. Later, we establish a comparison theorem for the solution of SGBH equation having higher order nonlinearities and it plays a crucial role in this work. Then, we discuss the weak differentiability of the solution to SGBH equation in the Malliavin calculus sense. Finally, we obtain the absolute continuity of the law of the solution with respect to the Lebesgue measure on $\mathbb{R}$, and the existence of density with the aid of comparison theorem and weak differentiability of the solution.
