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math.PR2024
An existence and uniqueness theory to stochastic partial differential equations involving pseudo-differential operators driven by space-time white noise
Jae-Hwan Choi, Ildoo Kim
In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operator…
math.AP2024
An existence and uniqueness result to evolution equations with sign-changing pseudo-differential operators and its applications to logarithmic Laplacian operators and second-order differential operators without ellipticity
Jae-Hwan Choi, Ildoo Kim
We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This…