RT info:eu-repo/semantics/article
T1 Mathematical properties and numerical approximation of pseudo-parabolic systems
A1 Abreu, Eduardo
A1 Cuesta Montero, Eduardo
A1 Durán Martín, Ángel
A1 Lambert, Wanderson
K1 Matemática aplicada
K1 Pseudo-paraboic systems; spectral approxinmations
K1 1206.13 Ecuaciones Diferenciales en Derivadas Parciales
AB The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem (ibvp) with Dirichlet boundary conditions are first studied. They include the weak formulation, well- posedness and existence of traveling wave solutions connecting two states, when the equations are considered as a variant of a conservation law. Then, the numerical approximation consists of a spectral approximation in space based on Legendre polynomials along with a temporal discretization with strong stability preserving (SSP) property. The convergence of the semidiscrete approximation is proved under suitable regularity conditions on the data. The choice of the temporal discretization is justified in order to guarantee the stability of the full discretization when dealing with nonsmooth initial conditions. A computational study explores the performance of the fully discrete scheme with regular and nonregular data.
PB Elsevier
SN 0898-1221
YR 2024
FD 2024-07-01
LK https://uvadoc.uva.es/handle/10324/73292
UL https://uvadoc.uva.es/handle/10324/73292
LA spa
NO Computers & Mathematics with Applications, July 2024,165, p. 163-179.
NO Producción Científica
DS UVaDOC
RD 19-jul-2025