The Tricomi problem for the Lavrent'ev--Bitsadze equation with retarded argument
type: Item
instance of: scholarly article
title: The Tricomi problem for the Lavrent'ev--Bitsadze equation with retarded argument
zbMATH Open document ID: 1027.35082
DOI: 10.1023/A:1012573829387
author: E. I. Moiseev
author: A. N. Zarubin
published in: Differential Equations
publication date: 2003-05-25T00:00:00Z
review text: For the Lavrent'ev-Bitsadze equation with retarded argument \[ u_{xx}(x,y)+(\operatorname {sgn}x)u_{yy}(x,y)-H(x-\tau)u(x-\tau ,y)=0, \] where \(0<\tau\) and \(H(\xi)\) is the Heaviside function, the authors consider the following BVP: Find a solution of the above equation in the domain \(D=\{0<x<\infty\), \(0<y<\pi \}\cup \{-\frac{\pi }{2}<x<0\), \(-x<y<\pi +x\}\), which satiesfies the boundary conditions \(u(x,0)=u(x,\pi)=0,0<x<\infty\); \(u(-y,y)=\psi (y)\), \(0<y<\pi /2\); \(\lim u(x,y)=0\), \(0<y<\pi /2\), \(x\rightarrow \infty\). Using some appropriate integral equations, the uniqueness of the solution for \(\tau \leq \sqrt{2}\) is proved. Construction of a solution is given by its appropriate representation with some biorthogonal series.
Mathematics Subject Classification ID: 35M10
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35C10
zbMATH DE Number: 1915931
zbMATH Keywords: biorthogonal series
reviewed by: N. Popivanov
MaRDI profile type: Publication
full work available at URL: a:1012573829387
OpenAlex ID: W142322869
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description: scientific article; zbMATH DE number 1915931