Abstract

The main goal of this work is to relate weak and pathwise mild solutions for parabolic quasilinear stochastic partial differential equations (SPDEs). Extending in a suitable way techniques from the theory of nonautonomous semilinear SPDEs to the quasilinear case, we prove the equivalence of these two solution concepts.

中文翻译：

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关于拟线性SPDE的路径弱解和弱解的等价性

摘要

这项工作的主要目标是关联抛物线拟线性随机偏微分方程 (SPDE) 的弱解和路径温和解。以合适的方式将技术从非自治半线性 SPDE 理论扩展到拟线性情况，我们证明了这两个解决方案概念的等价性。