Transformation of approximate solutions of linear parabolic equations into asymptotic solutions of quasilinear parabolic equations
type: Item
instance of: scholarly article
title: Transformation of approximate solutions of linear parabolic equations into asymptotic solutions of quasilinear parabolic equations
zbMATH Open document ID: 0838.35058
DOI: 10.1007/BF02266698
published in: Mathematical Notes
publication date: 1996-01-08T00:00:00Z
review text: We present formulas that express the solution of the quasilinear equation \(z_\delta- \varepsilon(K(z) z_\xi)_\xi= 0\) in terms of the solution to the linear equation with variable coefficients \(u_t- \varepsilon \mu u_{xx}= C\), where \(\mu= \mu(x, t, \varepsilon)= \mu_0(x, t)+ \mu_1(x, t)+\cdots\) is a function to be determined. As a special case, the collection of formulas relate soutions of simple wave type (functions of arguments \(x+ bt\), \(b=\text{const}\)), quasilinear equations, and semilinear parabolic equations.
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35A22
zbMATH DE Number: 830777
author: K. A. Volosov
MaRDI profile type: Publication
cites work: Q3789180
description: scientific article; zbMATH DE number 830777