Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application
Lp-Lq estimates of solutions to the damped wave equation in 3-dimensional space and their application
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DOI：
10.1007/s00209-003-0516-0
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发表时间：
2003-07
影响因子：
0.8
通讯作者：
K. Nishihara
中科院分区：
文献类型：
--
作者：
K. Nishihara
可以断言阻尼波动方程具有扩散结构ast→∞。在本文中，我们考虑线性阻尼波动方程和相应的抛物线方程的3维空间中的柯西问题，并获得每个解之差的Lp−Lq估计，其精确地代表了断言。分析了解的显式公式进行证明。第二个目标是将 Lp−Lq 估计值应用于具有功率非线性的半线性阻尼波动方程。如果幂大于藤田指数，则证明小弱解的时间全局存在性，并得到其最优衰减阶数。
It has been asserted that the damped wave equation has the diffusive structure ast→∞. In this paper we consider the Cauchy problem in 3-dimensional space for the linear damped wave equation and the corresponding parabolic equation, and obtain theLp−Lqestimates of the difference of each solution, which represent the assertion precisely. Explicit formulas of the solutions are analyzed for the proof. The second aim is to apply theLp−Lqestimates to the semilinear damped wave equation with power nonlinearity. If the power is larger than the Fujita exponent, then the time global existence of small weak solution is proved and its optimal decay order is obtained.