The Gauss center research in multiscale scientific computation.
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The problem of data assimilation for soil water movement
The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
The Rothe method for solving the first initial-boundary value problem for the equation of filtration in a cracked porous medium.
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the...
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for...
Thermal characterizations of exponential fin systems.
Thermal radiation and buoyancy effects on heat and mass transfer over a semi-infinite stretching surface with suction and blowing.
Two methods for solving an initial-boundary value problem for a system of Saint-Venant equations.