4 papers
Well-Posedness for Cauchy Problems with Singular Time-Measurable Pseudo-Differential Operators in Quasi-decreasing Weighted -Spaces
Jae-Hwan Choi, Ildoo Kim
This study examines Cauchy problems governed by highly singular, time-measurable pseudo-differential operators (singular measurable families of Fourier multipliers). We show that t…
Well-Posedness Of Second-Order Evolution Equations With Non-Integrable And Degenerate Coefficients In Weighted Lp-Spaces
Ildoo Kim, Kyeong-Hun Kim
We study the Cauchy problem for inhomogeneous evolution equations with time-dependent, potentially degenerate, and unbounded coefficients. A key feature of our work is allowing the…
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…
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…