Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations
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.
- Publication:
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arXiv e-prints
- Pub Date:
- June 1993
- DOI:
- 10.48550/arXiv.chao-dyn/9306008
- arXiv:
- arXiv:chao-dyn/9306008
- Bibcode:
- 1993chao.dyn..6008B
- Keywords:
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- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 29 pages