Conejero, J. Alberto; Lizama, Carlos; Ródenas Escribá, Francisco de Asís(Natural Sciences Publishing, 2015-09)
[EN] We study a third-order partial differential equation in the form
$\tau u_{ttt} +\alpha u_{tt} -c^2 u_{xx} -b u_{xxt} =0, (1)$$
that corresponds to the one-dimensional version of the Moore-Gibson-Thompson equation ...
[EN] We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden-Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the ...
[EN] During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the ...
Lizama, Carlos; Murillo Arcila, Marina(American Institute of Mathematical Sciences, 2022-08)
[EN] We study discrete time maximal regularity in Lebesgue spaces of sequences for time-stepping schemes arising from Lubich's convolution quadrature method. We show minimal properties on the quadrature weights that ...
Lizama, Carlos; Murillo Arcila, Marina; Peris Manguillot, Alfredo(American Institute of Physics, 2020-10)
[EN] We characterize for the first time the chaotic behavior of nonlocal operators that come from a broad class of time-stepping schemes of approximation for fractional differential operators. For that purpose, we use ...
[EN] We show the remarkable fact that the nonlocal property of the discrete N dimensional fractional Laplacian acting in the second variable of the lattice N x Z(N) can be exchanged with an equivalent memory corresponding ...
Conejero Casares, José Alberto; Lizama, Carlos; Murillo Arcila, Marina(Elsevier, 2016)
We study the viscous van Wijngaarden–Eringen equation:
∂2u
∂t2 − ∂2u
∂x2 = (Red)−1 ∂3u
∂t∂x2 + a2
0
∂4u
∂t2∂x2 (1)
which corresponds to the linearized version of the equation that models the acoustic planar
propagation ...