A nonlocal problem with integral conditions for a quasilinear hyperbolic equation
type: Item
instance of: scholarly article
title: A nonlocal problem with integral conditions for a quasilinear hyperbolic equation
zbMATH Open document ID: 1031.35108
DOI: 10.1023/A:1010226002462
author: Yanyan Li
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: This paper is devoted to a quasilinear equation of hyperbolic type with integral conditions. Indeeds the author considers the equation \[ u_{xy}+ (Au)_x+ (Bu)_y+ Cu= f(x, y, u),\tag{1} \] whose coefficients \(A(x,y)\), \(B(x,y)\) and \(C(x,y)\) are bounded and have bounded derivatives of first-order and the coefficient \(C(x,y)\) has also a bounded mixed derivative in the rectangle \(\{(x,y)\mid 0< x< a, 0< y< b\}\). The author studies existence and uniqueness of a generalized solution of (1) satisfying the conditions \[ \int^a_0 u(x,y) dy= \psi(y),\quad \int^b_0 u(x,y) dy= \varphi(x). \]
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 1927767
zbMATH Keywords: existence and uniqueness
zbMATH Keywords: generalized solution
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: a:1010226002462
OpenAlex ID: W168912298
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description: scientific article; zbMATH DE number 1927767