Abstract
In this paper, we study the initial boundary value problem of the wave equation with singular nonlinearities of the form
We prove decay estimates using multiplier method and weighted integral inequalities. We show that the energy of the system is bounded above by a quantity, depending on σ,g,r and α, which tends to zero (as time goes to infinity). We give many significant examples to illustrate how to derive from our general estimates the polynomial, exponential or logarithmic decay.
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Benaissa, A., Maatoug, A. Energy Decay Rate of Solutions for the Wave Equation with Singular Nonlinearities. Acta Appl Math 113, 117–127 (2011). https://doi.org/10.1007/s10440-010-9588-0
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DOI: https://doi.org/10.1007/s10440-010-9588-0
Keywords
- Wave equation
- Weakly nonlinear dissipative term
- Singular nonlinearities
- Multiplier method
- Integral inequalities