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November  2003, 3(4): 565-588. doi: 10.3934/dcdsb.2003.3.565

Decay of solutions to nonlinear parabolic equations: renormalization and rigorous results

H. Merdan 1, and  G. Caginalp 2,

1. 

Department of Mathematics, University of Pittsburg, Pittsburgh, PA 15260, United States
2. 

Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, United States

Received  February 2003 Revised  May 2003 Published  August 2003

Scaling and renormalization group (RG) methods are used to study parabolic equations with a small nonlinear term and find the decay exponents. The determination of decay exponents is viewed as an asymptotically self similar process that facilitates an RG approach. These RG methods are extended to higher order in the small coefficient of the nonlinearity. The RG results are verified in some cases by rigorous proofs and other calculational methods.
Keywords: asymptotic self-similarity., Renormalization group, nonlinear parabolic equations, decay of solutions, asymptotic analysis.
Mathematics Subject Classification: 35K55, 35K05, 35K15, 82B28, 41A6.
Citation: H. Merdan, G. Caginalp. Decay of solutions to nonlinear parabolic equations: renormalization and rigorous results. Discrete and Continuous Dynamical Systems - B, 2003, 3 (4) : 565-588. doi: 10.3934/dcdsb.2003.3.565
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