Complex Analysis

Journal of Contemporary Mathematical Analysis

, Volume 43, Issue 6, pp 353-364

First online:

Rational approximation and universality for a quasilinear parabolic equation

  • P. M. GauthierAffiliated withUniversité de Montréal Email author 
  • , N. TarkhanovAffiliated withInstitut für Mathematik, Universität Potsdam

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Abstract

Approximation theorems, analogous to results known for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for one of the simplest examples of a nonlinear partial differential equation, Burgers’ equation.

Key words

Cole-Hopf transformation Runge universality

MSC2000 numbers

Primary 41A20, 35J60 Secondary 41-XX