Cícero Lopes Frota

Fractional telegraph equations

We investigate several aspects of the fractional telegraph equations, in an effort to better understand the anomalous diffusion processes observed in blood flow experiments. In the earlier work Eckstein et al. [Electron. J. Differential Equations Conf. 03 (1999) 39–50], the telegraph equation D 2 u + 2aDu + Au = 0 was used, where D = d/dt ,a nd it was shown that, as t tends to infinity, u is approximated by v ,w here 2aDv + Av = 0; here A =− d 2 /dx 2 on L 2 (R) ,o rA can be a more general nonnegative selfadjoint operator. In this paper the concern is with the fractional telegraph equation E 2 u + 2aEu + Au = 0, where E = D γ and 0

Uniform Stabilization for a Hyperbolic Equation with Acoustic Boundary Conditions in Simple Connected Domains

We prove the existence and uniqueness of strong and weak solutions as well as the uniform stabilization of the energy of initial boundary value problem for a hyperbolic equation in a class of domains Ω ⊂ \( \Omega \subset \mathbb{R}^N \) which includes simply connected regions. The boundary Γ of Ω can be a smooth simple connected manifold and the boundary conditions are acoustic boundary conditions on a portion Γ1 of the boundary and the Dirichlet boundary condition on the rest of Γ.