A note on initial value problem for the generalized Tricomi equation in a mixed-type domain

Autor:	Kangqun Zhang
Rok vydání:	2013
Předmět:	Applied Mathematics General Mathematics Mathematical analysis Term (logic) Expression (computer science) Domain (mathematical analysis) Euler–Tricomi equation symbols.namesake Transformation (function) Hadamard transform Line (geometry) symbols Applied mathematics Initial value problem Mathematics
Zdroj:	Acta Mathematica Sinica, English Series. 29:1581-1596
ISSN:	1439-7617 1439-8516
DOI:	10.1007/s10114-013-2123-2
Popis:	In this paper, we study the well-posedness of initial value problem for n-dimensional generalized Tricomi equation in the mixed-type domain {(t, x): t ∈ [−1,+∞), x ∈ ℝn} with the initial data given on the line t = −1 in Hadamard’s sense. By taking partial Fourier transformation, we obtain the explicit expression of the solution in terms of two integral operators and further establish the global estimate of such a solution for a class of initial data and source term. Finally, we establish the global solution in time direction for a semilinear problem used the estimate.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::da979eafdfa8a8675ef3cb2c1b72eb34 https://doi.org/10.1007/s10114-013-2123-2 Zobrazit plný text záznamu Plný text ve formátu PDF