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

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概要

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• 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) ≥ V0(1 + |x|2)−1/2 (see condition (A) below). The solutions manifest a new threshold effect with respect to the size of the coefficient V0: for 1 < V0 < N the energy decay rate is exactly t−V0, while for V0 ≥ N the energy decay rate coincides with the decay rate of the corresponding parabolic problem.

著者

• Ikehata Ryo

  Department Of Mathematics Faculty Of School Education Hiroshima University

• Yordanov Borislav

  Department of Mathematics, University of Tennessee

• TODOROVA Grozdena

  Department of Mathematics, University of Tennessee

関連論文

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• ENERGY DECAY FOR THE WAVE EQUATIONS OF KIRCHHOFF TYPE WITH LINEAR DAMPING TERMS
• Optimal decay rate of the energy for wave equations with critical potential
• Optimal decay rate of the energy for wave equations with critical potential

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