On conditions of solvability of the Goursat problem for generalized Aller equation
type: Item
instance of: scholarly article
title: On conditions of solvability of the Goursat problem for generalized Aller equation
zbMATH Open document ID: 1400.35172
DOI: 10.3103/S1066369X18080030
author: V. I. Zhegalov
author: E. A. Utkina
author: I. M. Sarvarova
published in: Russian Mathematics
publication date: 2018-10-12T00:00:00Z
review text: The authors consider a Goursat problem in a rectangle domain \(D\subset {{\mathbb{R}}^{2}}\) for the equation \[ u_{xxy}+ mu_{xx}+ nu_{xy}+pu_{x}+qu_y+ru = f \] which is a generalization of the Aller equation \(u_t=(mu_x+bu_{xt})_x\), an important model of soil moisture transfer process in aeration zones. The authors obtain 16 variants of conditions concerning the coefficients of the considered equation such that every one of them guaranty the resolvability of this equation in quadrature. Note that every collection consists of three identities which interconnect the five coefficients appearing in left-hand side of an equation.
reviewed by: Andrey Zahariev
Mathematics Subject Classification ID: 35K70
zbMATH DE Number: 6952508
zbMATH Keywords: Aller equation
zbMATH Keywords: Goursat problem
zbMATH Keywords: factorization
MaRDI profile type: Publication
cites work: Pseudoparabolic equations in one space variable
cites work: Remarks Concerning the Supports of Solutions of Pseudoparabolic Equations
cites work: The Uniqueness Class for the Cauchy Problem for Pseudoparabolic Equations
cites work: Q3738808
cites work: Q3478846
cites work: On a nonlocal boundary value problem with variable coefficients for the heat equation and the Aller equation
cites work: Q5186065
cites work: Q4390818
cites work: On problems reduced to the Goursat problem for a third order equation
cites work: Q5228636
cites work: Pseudoparabolic equation of the third order
cites work: Differential equations with highest partial derivatives
full work available at URL: s1066369x18080030
OpenAlex ID: W2884212283
description: scientific article; zbMATH DE number 6952508