Related papers: Initial-boundary value problems for conservation l…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
Due to the absence of dynamical equation in the vertical momentum component of the primitive equations (PEs) of atmospheric dynamics, the vertical component of the velocity can be recovered only from the information on the other physical…
Evolution PDEs for dispersive waves are considered in both linear and nonlinear integrable cases, and initial-boundary value problems associated with them are formulated in spectral space. A method of solution is presented, which is based…
We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order 1/3 in the interior of the…
We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyperbolic initial boundary value problems with open…
Motivated by an analysis on the well-posedness of the initial boundary value problem for the motion of an inextensible hanging string, we first consider an initial boundary value problem for one-dimensional degenerate hyperbolic systems…
In this paper, we discuss an initial-boundary value problem (IBVP) for the multi-term time-fractional diffusion equation with x-dependent coefficients. By means of the Mittag-Leffler functions and the eigenfunction expansion, we reduce the…
We present a straightforward energy stable weak implementation procedure of open boundary conditions for nonlinear initial boundary value problems. It simplifies previous work and its practical implementation.
In this paper, we consider the initial-boundary value problem of the nonhomogeneous primitive equations with density-dependent viscosity. Local well-posedness of strong solutions is established for this system with a natural compatibility…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating…
The initial-dynamic boundary value problem (idbvp) for the complex Ginzburg-Landau equation (CGLE) on bounded domains of $\mathbb{R}^N$ is studied by converting the given mathematical model into a Wentzell initial-boundary value problem…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
An initial-boundary value problem in a strip with homogeneous Diriclet boundary conditions for two-dimensional generalized Zakharov-Kuznetsov equation is considered. In particular, dissipative and absorbing degenerate terms can be…
We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
In recent work, we used pseudo-differential theory to establish conditions that the initial-boundary value problem for second order systems of wave equations be strongly well-posed in a generalized sense. The applications included the…
In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg- de Vries equation posed on a finite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2…
This paper concerns the initial-boundary value problem to 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global weak solution. The main idea of this paper is…