Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation
Optimal Regularity and Long-Time Behavior of Solutions for the Westervelt Equation
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DOI：
10.1007/s00245-011-9138-9
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发表时间：
2011-06
影响因子：
1.8
通讯作者：
S. Meyer;M. Wilke
中科院分区：
文献类型：
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作者：
S. Meyer;M. Wilke
本文研究了拟线性Westerpyrutone方程的初边值问题，该方程模拟了流体介质中的声传播。我们证明了，如果初始数据是足够小的和正规的，那么存在唯一的全局解具有最优Lp-正则性。我们进一步表明，该解决方案收敛到零的时间趋于无穷大的指数率。我们的技巧是基于抽象拟线性抛物方程的极大Lp正则性。
We investigate an initial-boundary value problem for the quasilinear Westervelt equation which models the propagation of sound in fluidic media. We prove that, if the initial data are sufficiently small and regular, then there exists a unique global solution with optimalLp-regularity. We show furthermore that the solution converges to zero at an exponential rate as time tends to infinity. Our techniques are based on maximalLp-regularity for abstract quasilinear parabolic equations.