Optimal decay rate of the energy for wave equations with critical potential

Ryo Ikehata; Grozdena Todorova; Borislav Yordanov

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Optimal decay rate of the energy for wave equations with critical potential

机译：具有临界势的波动方程的能量最优衰减率

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摘要

We study the long time behavior of solutions of the wave equation with a variable damping term V(x)_(ut) in the case of critical decay V(x) ≥ V_0(1 + |x|~2)~(-1/2) (see condition (A) below). The solutions manifest a new threshold effect with respect to the size of the coefficient V_0: for 1 < V_0 < N the energy decay rate is exactly t~(-V_0), while for V_0 ≥ N the energy decay rate coincides with the decay rate of the corresponding parabolic problem.

机译：在临界衰减V（x）≥V_0（1 + | x |〜2）〜（-1）的情况下，我们研究了具有可变阻尼项V（x）_（ut）的波动方程解的长时间行为。 / 2）（请参阅下面的条件（A））。这些解相对于系数V_0的大小表现出新的阈值效应：对于1

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来源
《Journal of the Mathematical Society of Japan》 |2013年第1期|183-236|共54页
作者
Ryo Ikehata; Grozdena Todorova; Borislav Yordanov;
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作者单位

Department of Mathematics Graduate School of Education Hiroshima University Higashi-Hiroshima 739-8524, Japan;

Department of Mathematics University of Tennessee Knoxville, USA;

Department of Mathematics University of Tennessee Knoxville, USA;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
damped wave equation; critical potential; energy decay; finite speed of propagation; diffusive structure;

机译：阻尼波方程临界潜力;能量衰减有限的传播速度;扩散结构;

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6. Global Existence and Energy Decay Rates for a Kirchhoff-Type Wave Equation with Nonlinear Dissipation [O] . Daewook Kim, Dojin Kim, Keum-Shik Hong, -1

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7. Optimal decay rate of the energy for wave equations with critical potential [O] . Ryo IKEHATA, Grozdena TODOROVA, Borislav YORDANOV 2013

机译：具有临界潜力的波动方程能量的最佳衰减率

Optimal decay rate of the energy for wave equations with critical potential

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