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Volume 17, Issue 3
Asymptotic Behavior of the Nonlinear Parabolic Equations

Boqing Dong

J. Part. Diff. Eq., 17 (2004), pp. 255-263.

Published online: 2004-08

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  • Abstract

This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2})}. The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.

  • Keywords

L² decay spectral decomposition nonlinear parabolic equation

  • AMS Subject Headings

35K15 35B40

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-17-255, author = {Boqing Dong }, title = {Asymptotic Behavior of the Nonlinear Parabolic Equations}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {3}, pages = {255--263}, abstract = {

This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2})}. The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5391.html} }
TY - JOUR T1 - Asymptotic Behavior of the Nonlinear Parabolic Equations AU - Boqing Dong JO - Journal of Partial Differential Equations VL - 3 SP - 255 EP - 263 PY - 2004 DA - 2004/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5391.html KW - L² decay KW - spectral decomposition KW - nonlinear parabolic equation AB -

This paper is concerned with the large time behavior for solutions of the nonlinear parabolic equations in whole spaces R^n. The spectral decomposition methods of Laplace operator are applied and it is proved that if the initial data u_0 ∈ L² ∩ L^r for 1 ≤ r ≤ 2, then the solutions decay in L² norm at t^{-\frac{n}{2}(\frac{1}{r}-\frac{1}{2})}. The decay rates are optimal in the sense that they coincide with the decay rates of the solutions to the heat equations with the same initial data.

Boqing Dong . (2004). Asymptotic Behavior of the Nonlinear Parabolic Equations. Journal of Partial Differential Equations. 17 (3). 255-263. doi:
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