This paper investigates the Cauchy problem to a class of stochastic non-autonomous evolution equations of parabolic type governed by noncompact evolution families in Hilbert spaces. Combining the theory of evolution families, the fixed point theorem with respect to convex-power condensing operator and a new estimation technique of the measure of noncompactness, we established some new existence results of mild solutions under the situation that the nonlinear function satisfy some appropriate local growth condition and a noncompactness measure condition. Our results generalize and improve some previous results on this topic, since the strong restriction on the constants in the condition of noncompactness measure is completely deleted, and also the condition of uniformly continuity of the nonlinearity is not required. At last, as samples of applications, we consider the Cauchy problem to a class of stochastic non-autonomous partial differential equation of parabolic type.

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由非紧致演化族控制的随机非自治演化方程的柯西问题

本文研究了希尔伯特空间中一类由非紧致演化族控制的抛物型随机非自治演化方程的柯西问题。结合演化族理论，凸幂凝聚算子的不动点定理和非紧致性测度的新估计技术，在非线性函数满足一定局部性的情况下，建立了温和解的一些新存在结果。生长条件和非紧实度测量条件。我们的结果归纳并改进了有关该主题的先前结果，因为完全消除了非紧致性度量条件下对常数的强约束，并且也不需要非线性连续一致的条件。最后，