Remarks on the behavior of solutions to the linear wave equations inunbounded domains

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概要

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• Uniform L^2 decay of solutions for the linear dissipative wave equations will be given in a particular case when the initial data belongs to a manifold in L^2 (Ω)×L^2 (Ω). For this, we employ the modified method of Morawetz [7]. Furthermore, this technique will be applicable to obtain L^2 bound for the solutions to the free wave equations without any support compact condition of the initial data in exterior domains. As an application of this estimate, a simplified alternative proof for the local energy decay will be discussed. Finally, we shall remark the L^2 decay or bound under some additional conditions on the initial data, which is also an natural extension of the result of Kawashima et. al.[3]

• 東海大学の論文

著者

• Ikehata Ryo

  Department Of Mathematics Faculty Of School Education Hiroshima University

• Matsuyama Tokio

  Department of Mathematics,School of Science, Tokai University

• Matsuyama Tokio

  Department Of Mathematics School Of Science Tokai University

• Matsuyama Tokio

  Department Of Mathematics Faculty Of Science Tokai University

• Ikehata Ryo

  Department of Mathematics,Faculty of School Education, Hiroshima University

関連論文

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• Remarks on the behavior of solutions to the linear wave equations inunbounded domains
• The Palais-Smale condition for the energy of some semilinear parabolic equations
• L^2-BEHAVIOUR OF SOLUTIONS TO THE LINEAR HEAT AND WAVE EQUATIONS IN EXTERIOR DOMAINS
• Decay estimates of solutions for dissipative wave equations in R^N with lower power nonlinearities
• 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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