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

H. Merdan; G. Caginalp

doi:10.3934/dcdsb.2003.3.565

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2003, Volume 3, Issue 4: 565-588. Doi: 10.3934/dcdsb.2003.3.565

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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
2.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260

Received: January 31, 2003

Revised: April 30, 2003

Published: October 2003

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Abstract

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.

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Mathematics Subject Classification: 35K55, 35K05, 35K15, 82B28, 41A60.

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