The Threshold between Effective and Noneffective Damping for Semilinear Waves

By M. DʼAbbicco. 2012

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In this paper we study the global existence of small data solutions to the Cauchy problem utt −△u+ μ 1 + t ut = f(t, u) , u(0, x) = u0(x) , ut(0, x) = u1(x) , where μ ≥ 2. We obtain estimates for the solution and its energy with the same decay rate of the linear problem. We extend our results to a model with polynomial speed of propagation, and to a model with an exponential speed of propagation and a constant damping ν ut.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1e11687ddd1d89203309d0ebbb6ad4f0cd1a64e4