2024/12/04 by Ruy Coimbra Charão, Charão, Ruy Coimbra, Ryo Ikehata +1
Physics and Astronomy · Mathematics · Engineering · #Nonlinear Photonic Systems #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2412.03091
We consider damped wave equations with a potential and rotational inertia terms. We study the Cauchy problem for this model in the one dimensional Euclidean space and we obtain fast energy decay and L2-decay of the solution itself as time goes to infinity. Since we are considering this problem in the one dimensional space, we have no useful tools such as the Hardy and/or Poincaré inequalities. This causes significant difficulties to derive the decay property of the solution and the energy. A potential term will play a role for compensating these weak points.