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

Autor:	Choi, Jae-Hwan, Kim, Ildoo
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs 35S05 35S10 35A01 35D30 47G30
Druh dokumentu:	Working Paper
Popis:	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 formulation is applicable to evolution equations involving pseudo-differential operators, even when the signs of their symbols may vary over time. Notably, our main operator includes the logarithmic Laplacian operator $\log (-\Delta)$ and a second-order differential operator whose leading coefficients are not positive semi-definite. Comment: 49 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.19968 Zobrazit plný text záznamu View this record from Arxiv