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The numerical matrix Numerov algorithm is used to solve the stationary Schr\"odinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the…
We investigate the Riemann problem for the shallow water equations with variable and (possibly) discontinuous topography and provide a complete description of the properties of its solutions: existence; uniqueness in the non-resonant…
This paper is devoted to establishing the convergence rate of the hypersonic similarity for the inviscid steady irrotational Euler flow over a two-dimensional Lipschitz slender wedge in $BV\cap L^1$ space. The rate we established is the…
In this paper we are concerned with the convergence rate of solutions to the three-dimensional turbulent flow equations. By combining the $L^p$-$L^q$ estimates for the linearized equations and an elaborate energy method, the convergence…
In this paper, we examine the question of the boundary controllability of the one-dimensional non-isentropic Euler equation for compressible polytropic gas, in the context of weak entropy solutions. We consider the system in Eulerian…
We show that a specific skew-symmetric form of nonlinear hyperbolic problems leads to energy and entropy bounds. Next, we exemplify by considering the compressible Euler equations in primitive variables, transform them to skew-symmetric…
We give a solution of the Riemann problem in relativistic hydrodynamics in the case of ultrarelativistic equation of state and nonvanishing components of the velocity tangent to the initial discontinuity. Simplicity of the…
Based on a comparison principle, we derive an exponential rate of convergence for solutions to the initial-boundary value problem for a class of quasilinear parabolic equations in one space dimension. We then apply the result to some models…
The ultra-relativistic Euler equations for an ideal gas are described in terms of the pressure $p$, the spatial part $\underline{u} \in \R^3$ of the dimensionless four-velocity and the particle density $n$. Radially symmetric solutions of…
This article addresses a fundamental concern regarding the incompressible approximation of fluid motions, one of the most widely used approximations in fluid mechanics. Common belief is that its accuracy is $O(\epsilon)$ where $\epsilon$…
We propose a new concept of (S)-convergence applicable to numerical methods as well as other consistent approximations of the Euler system in gas dynamics. (S)-convergence, based on averaging in the spirit of Strong Law of Large Numbers,…
We proved that for the countably infinite number of one-parameterized one dimensional dynamical systems, they preserve the Lebesgue measure and they are ergodic for the measure (infinite ergodicity). Considered systems connect the parameter…
This article concerns a scalar multidimensional conservation law where the flux is of Panov type and may contain spatial discontinuities. We define a notion of entropy solution and prove that entropy solutions are unique. We propose a…
In this paper, we present an efficient numerical method to address a thermodynamically consistent gas flow model in porous media involving compressible gas and deformable rock. The accurate modeling of gas flow in porous media often poses…
We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
The thermodynamic maximum principle for the Boltzmann-Gibbs-Shannon (BGS) entropy is reconsidered by combining elements from group and measure theory. Our analysis starts by noting that the BGS entropy is a special case of relative entropy.…
We investigate the relaxation problem and the diffusion phenomenon for the compressible Euler system with a time-dependent damping coefficient of the form $\tfrac{\mu}{(1+t)^{\lambda}}$ in $\mathbb{R}^d$ $(d \geq 1)$. We establish uniform…
We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…
By intentionally underestimating the rate of convergence of exact-diagonalization values for the mass or energy gaps of finite systems, we form families of sequences of gap estimates. The gap estimates cross zero with generically nonzero…