We study a Riemann problem for the two-dimensional isentropic gas dynamics equations which models transonic regular reflection. When written in self-similar coordinates, the system changes type from hyperbolic to mixed hyperbolic-elliptic. Using the theory of one-dimensional hyperbolic conservation laws, we formulate a free boundary problem in the subsonic region and we outline the main ideas f...

It is considered the hyperbolic-parabolic approximation

A Riemann surface is called pseudo-real if it admits anticonformal automorphisms but no anticonformal involution. Pseudo-real Riemann surfaces appear in a natural way in the study of the moduli space MKg of Riemann surfaces considered as Klein surfaces. The moduli space Mg of Riemann surfaces of genus g is a two-fold branched covering of MKg , and the preimage of the branched locus consists of ...

in this paper, we present recent results in integral inequality theory. our results are based on thefractional integration in the sense of riemann-liouville

The goal of this paper is to make mathematically precise, then illustrate, how to “email” a Riemann surface. We assume each of our Riemann surfaces are orientable and connected. We will follow the notation from [2] and will cite theorems from this source whenever possible. To email a Riemann surface we want a unique Riemann surface to correspond to a set L of finitely many matrices whose entrie...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected...

As a basic model, the fourth-order quasilinear thin film equation (the TFE– 4) with a concentration-dependent doubly degenerate mobility coefficient vanishing at two equilibrium levels u = ±1, ut = −(|1− u|uxxx)x , is studied. The basic Riemann problem for the TFE–4 with discontinuous initial data

We deal with initial-boundary value problems for systems of conservation laws in one space dimension and we focus on the so-called boundary Riemann problem. It is known that, in general, different viscous approximations provide different limits. We establish sufficient conditions to conclude that two different approximations lead to the same limit. As an application of this result, we show that...