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Existence results for linear evolution equations of parabolic type

This research was partially supported by Q-PIT, Kyushu University

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  • We study a stochastic parabolic evolution equation of the form $ dX+AXdt = F(t)dt+G(t)dW(t)$ in Banach spaces. Existence of mild and strict solutions and their space-time regularity are shown in both the deterministic and stochastic cases. Abstract results are applied to a nonlinear stochastic heat equation.

    Mathematics Subject Classification: Primary: 47D06, 60H15; Secondary: 35R60.


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