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The existence and uniqueness of energy solutions to local non-Lipschitz stochastic evolution equations
Authors:Takeshi Taniguchi  
Institution:aDivision of Mathematical Sciences, Graduate School of Comparative Culture, Kurume University, Miimachi, Kurume, Fukuoka 839-8502, Japan
Abstract:Let H,V and K be separable Hilbert spaces. In this paper we consider the existence and uniqueness of energy solutions to the following stochastic evolution equation:
View the MathML source
where View the MathML source is a linear bounded operator with coercivity, monotone condition and hemicontinuity, View the MathML source and View the MathML source are measurable functions and satisfy the local non-Lipschitz condition proposed by the author T. Taniguchi, Successive approximations to solutions of stochastic differential equations, J. Differential Equations 96 (1992) 152–169].
Keywords:Stochastic evolution equations  Energy solutions  Local non-Lipschitz condition  Coercivity condition
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