Fokas method for linear boundary value problems involving mixed spatial derivatives

Autor:	Batal, Ahmet, Fokas, Athanassios S., Özsarı, Türker
Rok vydání:	2020
Předmět:	Mathematics - Analysis of PDEs Mathematics - Complex Variables 35A22 35C15 35G16 35K20 35K35 35Q41
Druh dokumentu:	Working Paper
DOI:	10.1098/rspa.2020.0076
Popis:	We obtain solution representation formulas for some linear initial boundary value problems posed on the half space that involve mixed spatial derivative terms via the unified transform method (UTM), also known as the Fokas method. We first implement the method on the second order parabolic PDEs; in this case one can alternatively eliminate the mixed derivatives by a linear change of variables. Then, we employ the method to biharmonic problems, where it is not possible to eliminate the cross term via a linear change of variables. A basic ingredient of the UTM is the use of certain invariant maps. It is shown here that these maps are well-defined provided that certain analyticity issues are appropriately addressed. Comment: 16 pages, 6 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2002.01057 Zobrazit plný text záznamu View this record from Arxiv