On the local well-posedness of randomly forced reaction-diffusion equations with L² initial data and a superlinear reaction term

Key Points

• The study aims to establish the well-posedness of a particular class of stochastic reaction-diffusion equations.
• Analyzed a parabolic stochastic partial differential equation (SPDE) on the interval [0, 1]
• Considered multiplicative space-time white noise for forcing
• Applied bounded and Lipschitz diffusion and locally Lipschitz drift coefficients
• Utilized L log L growth condition for analysis
• Proved that the SPDE is well-posed under L2 initial data conditions
• Resolved a strong form of an existing open problem in the field

Abstract