Long-time behavior for a nonlinear fourth-order parabolic equation
Long-time behavior for a nonlinear fourth-order parabolic equation
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DOI：
10.1090/s0002-9947-04-03528-7
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发表时间：
2004-08
影响因子：
1.3
通讯作者：
María J. Cáceres;J. Carrillo;G. Toscani
中科院分区：
文献类型：
--
作者：
María J. Cáceres;J. Carrillo;G. Toscani
研究了一类具有对数非线性项的四阶非线性退化扩散方程在周期边界条件下初边值问题解的渐近性。对于严格正且适当小的初始数据，我们证明了当时间趋于无穷大时，正解指数地逼近其平均值。这些结果是通过分析经解的对数验证的方程而得到的。
We study the asymptotic behavior of solutions of the initial-boundary value problem, with periodic boundary conditions, for a fourth-order nonlinear degenerate diffusion equation with a logarithmic nonlinearity. For strictly positive and suitably small initial data we show that a positive solution exponentially approaches its mean as time tends to infinity. These results are derived by analyzing the equation verified by the logarithm of the solution.