Global Solvability and Lp Decay for the Semilinear Dissipative Wave Equations in Four and Five Dimensions
Global Solvability and Lp Decay for the Semilinear Dissipative Wave Equations in Four and Five Dimensions
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DOI：
10.1619/fesi.49.215
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发表时间：
2006
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影响因子：
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通讯作者：
K. Ono
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文献类型：
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作者：
K. Ono
本文研究了半线性耗散波动方程（ε + ε t）u =（ε + ε t）u的Cauchy问题解的整体存在性、唯一性和渐近性|u| RN ×（0，∞）中的α+1，其中u| t=0= eu 0和tu|对于小参数e > 0，t=0 = eu 1。这里，我们不假设初始数据（u 0，u1）上的任何紧支撑条件。当维数N = 4，5且α大于一个临界数2/N（通常称为Fujita指数）时，我们解决了该问题的整体时间可解性问题，并得到了解的Lp模在p ≥ 1时的急剧衰减率.
We study the global existence, uniqueness, and asymptotic behavior of solutions to the Cauchy problem for the semilinear dissipative wave equations: (∅+∂t)u =|u|α+1 in RN × (0, ∞) with u|t=0=eu0 and ∂tu|t=0 = eu1 for a small parameter e > 0. Here, we do not assume any compactly support conditions on the initial data (u0, u1). When dimension N = 4, 5 and α is greater than a critical number 2/N which is often called Fujita's exponent, we solve the global in time solvability problem and we derive the sharp decay rates of Lp norm with p ≥ 1 of the solutions.