\(Q\)-conditional symmetry of the nonlinear \((1+2)\)--dimensional reaction-diffusion equations
type: Item
instance of: scholarly article
zbMATH Open document ID: 1289.35159
author: Nataliya Ichans'ka
publication date: 2013-09-26T00:00:00Z
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 6212598
zbMATH Keywords: symmetry analysis
zbMATH Keywords: reaction-diffusion equations
MaRDI profile type: Publication
title: \(Q\)-conditional symmetry of the nonlinear \((1+2)\)--dimensional reaction-diffusion equations
published in: Matematychnyĭ Visnyk Naukovogo Tovarystva Im. Shevchenka
review text: The author deals with a study of a class of \((1+2)\)-dimensional nonlinear reaction-diffusion equations NEWLINE\[NEWLINE H(u) u_0 + \Delta u = F(u), \tag{1} NEWLINE\]NEWLINE where \(u = u(x) \in \mathbb{R}^1\), \(x=(x_0, \vec x)\), \(\vec x \in \mathbb{R}^2\); \( H(u)\), \(F(u)\) are arbitrary smooth functions. She presents a complete description of \(Q\)-conditional invariant operators for the equations (1). The obtained symmetries are used for finding exact solutions of the equations under consideration and reduction of the equations to ordinary differential equations.
description: scientific article; zbMATH DE number 6212598