Renormalization-group and Asymptotics of Solutions of Nonlinear Parabolic Equations
(1994) Communications on Pure and Applied Mathematics — Vol. 47, n° 6, p. 893-922 (1994)
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- Abstract
- We present a general method for studying long-time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations, to boundary conditions at infinity creating a front, and to higher (possibly fractional) differential linear terms. We present in detail the analysis for nonlinear diffusion-type equations with initial data falling off at infinity and also for data interpolating between two different stationary solutions at infinity. In an accompanying paper, [5], the method is applied to systems of equations where some variables are ''slaved,'' such as the complex Ginzburg-Landau equation. (c) 1994 John Wiley & Sons, Inc.
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Bricmont, J., Kupiainen, A., & Lin, G. (1994). Renormalization-group and Asymptotics of Solutions of Nonlinear Parabolic Equations. Communications on Pure and Applied Mathematics, 47(6), 893-922. https://doi.org/10.1002/cpa.3160470606 (Original work published 1994)