Stochastic parabolic equations with singular potentials

Abstract

In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from the white noise analysis and the concept of very weak solutions. For given stochastic parabolic equation we introduce the notion of a stochastic very weak solution, prove the existence and uniqueness of the very weak solution to corresponding stochastic initial value problem and show its independence of a regularization on given singular potential. In addition, the consistency of a stochastic very weak solution with a stochastic weak solution is shown.

29 pages

References in corpus (6)

• Fractional Klein-Gordon equation with singular mass
• The heat equation with strongly singular potentials
• Stochastic evolution equations with multiplicative noise
• Stochastic evolution equations with Wick-polynomial nonlinearities
• Heat Equation With a Geometric Rough Path Potential in One Space Dimension: Existence and Regularity of Solution
• Fractional Schrödinger Equation with singular potentials of higher-order