Rational Approximation for a Quasilinear Parabolic Equation
P. M. Gauthier, N. Tarkhanov
TL;DR
This paper develops approximation theorems for solutions of the heat equation and extends these results to nonlinear parabolic equations like Burgers' equation using the Cole-Hopf transformation.
Contribution
It introduces approximation theorems for nonlinear parabolic equations by leveraging known results for linear elliptic equations and the Cole-Hopf transformation.
Findings
Established approximation theorems for the heat equation.
Extended approximation results to Burgers' equation.
Demonstrated the effectiveness of the Cole-Hopf transformation in this context.
Abstract
Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers' equation.
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Taxonomy
Topicsadvanced mathematical theories · Mathematical Analysis and Transform Methods · Advanced Mathematical Modeling in Engineering