Related papers: Asymptotic approximation of hyperbolic weakly nonl…

The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…

We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…

In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. We…

A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…

We prove the asymptotic functional Poisson laws in the total variation norm and obtain estimates of the corresponding convergence rates for a large class of hyperbolic dynamical systems. These results generalize the ones obtained before in…

We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interactions, respectively. Specifically, letting epsilon denote an…

In this paper we focus on the initial value problem for a hyperbolic-elliptic coupled system of a radiating gas in multi-dimensional space. By using a time-weighted energy method, we obtain the global existence and optimal decay estimates…

This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary…

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…

We study the Cowling approximation by analytical means as applied to a system of linear differential equations arising from models of non-radial stellar pulsation. We consider various asymptotic cases, including those of high harmonic…

In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…

We consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times. We are dealing with generic situations where the…

We consider a sequence of approximate solutions to the compressible Euler system admitting uniform energy bounds and/or satisfying the relevant field equations modulo an error vanishing in the asymptotic limit. We show that such a sequence…

We consider a layer of an inviscid fluid with free surface which is subject to vertical high-frequency vibrations. We derive three asymptotic systems of equations that describe slowly evolving (in comparison with the vibration frequency)…

An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems,…

We propose a numerical method to solve an inverse source problem of computing the initial condition of hyperbolic equations from the measurements of Cauchy data. This problem arises in thermo- and photo- acoustic tomography in a bounded…

We present a computational analysis of a 2$\times$2 hyperbolic system of balance laws whose solutions exhibit complex nonlinear behavior. Traveling-wave solutions of the system are shown to undergo a series of bifurcations as a parameter in…