Ultraparabolic Equations with Infinitely Increasing Coefficients in the Group of Lowest Terms and Degenerations in the Initial Hyperplane

Autor:	S. D. Ivasyshen, H. S. Pasichnyk
Rok vydání:	2020
Předmět:	Statistics and Probability Pure mathematics Hyperplane Group (mathematics) Applied Mathematics General Mathematics Bounded function Fundamental solution Function (mathematics) Type (model theory) Mathematics
Zdroj:	Journal of Mathematical Sciences. 249:333-354
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-020-04946-3
Popis:	We consider an ultraparabolic equation with lowest coefficients infinitely increasing as |x| → ∞ and degenerations for t = 0 . We find the fundamental solution G of this equation in the explicit form, establish the properties of the function G and, in particular, deduce exact estimates for G and its derivatives. By using these properties, we prove theorems on the integral representations of solutions of the inhomogeneous equation bounded as functions of x and such that their behavior as t → 0 depends on the type of degeneration of the equation for t = 0 .
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::db0f0303cb76b0d0736960b00ff9486c https://doi.org/10.1007/s10958-020-04946-3 Zobrazit plný text záznamu Plný text ve formátu PDF