106 citations · 730 across the 45 of their papers we have counts for
46 papers
A high-order regularization of the non-linear shallow water equations with weakly singular shock waves and its approximation by finite volume methods
Rezwana Razzaque Angana, Dimitrios Mitsotakis
Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant an…
Bona-Smith-type systems in bounded domains with slip-wall boundary conditions: Theoretical justification and a conservative numerical scheme
Dimitrios Antonopoulos, Dimitrios Mitsotakis
Considered herein is a class of Boussinesq systems of Bona-Smith type that describe water waves in bounded two-dimensional domains with slip-wall boundary conditions and variable b…
Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system
Daria Bolbot, Dimitrios Mitsotakis, Athanasios E. Tzavaras
The Serre-Green-Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre-Green-Naghdi system incorporati…
Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II. Dynamics
Jerry Bona, Angel Duran, Dimitrios Mitsotakis
Considered here are two systems of equations modeling the two-way propagation of long-crested, long-wavelength internal waves along the interface of a two-layer system of fluids in…
Equations for small amplitude shallow water waves over small bathymetric variations
Samer Israwi, Youssef Khalifeh, Dimitrios Mitsotakis
A generalized version of the -Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conserv…
Dispersive shocks in diffusive-dispersive approximations of elasticity and quantum-hydrodynamics
Daria Bolbot, Dimitrios Mitsotakis, Athanasios E. Tzavaras
The aim is to assess the combined effect of diffusion and dispersion on shocks in the moderate dispersion regime. For a diffusive dispersive approximation of the equations of one-d…