Abstract
In this article, we investigate the existence and uniqueness of local mild solutions for the one-dimensional generalized stochastic Burgers' equation (GSBE) containing a nonlinearity of polynomial type and perturbed by α-regular cylindrical Volterra process and having Dirichlet boundary conditions. The Banach fixed point theorem (or contraction mapping principle) is used to obtain the local solvability results. The L∞-estimate on both time and space for the stochastic convolution involving the α-regular cylindrical Volterra process is obtained with the help of Garsia-Rodemich-Rumsey inequality. Further, the existence and uniqueness of global mild solution of GSBE up to third order nonlinearity is also shown.
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