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Title Diffusion phenomenon for dissipative wave equations with two non-commuting operators

Name Grozdena H Todorova
Country USA
Email todorova@math.utk.edu
Co-Author(s) Petronela Radu, Borislav Yordanov
Submit Time 2014-03-28 20:07:58
Special Session 60: Recent advances in evolutionary equations
We consider the asymptotic behavior of solutions to dissipative wave equations involving two non-commuting self-adjoint operators in Hilbert space. The main result is that the abstract diffusion phenomenon takes place. We obtain precise estimates for consecutive diffusion approximations and remainder. In this process we use an abstract version of weighted estimates. When the diffusion semigroup has the Markov property, relying on the maximal regularity, we get sharp results. We apply the abstract results to derive optimal decay estimates for dissipative hyperbolic equations with variable coefficients in an exterior domain. Applications to nonlocal settings provide new decay rates for solutions of nonlocal dissipative wave equations.