Hyperbolic Systems Of Quasilinear Equations Research Articles

Averaging a High-Frequency Hyperbolic System of Quasilinear Equations with Large Summands

Averaging a High-Frequency Hyperbolic System of Quasilinear Equations with Large Summands

Hyperbolic systems of quasilinear equations in compressible fluid dynamics with an objective Cattaneo-type extension for the heat flux

We consider the coupling between the equations of motion of an inviscid compressible fluid in space with an objective Cattaneo-type extension for the heat flux. These equations are written in quasilinear form and we determine which of the given formulations for the heat flux allows for the hyperbolicity of the system. This feature is necessary for a physically acceptable sense of well-posedness for the Cauchy problem of such system of equations.

Classical solvability of a problem with moving boundaries for a hyperbolic system of quasilinear equations

Using the method of characteristics and the method of contracting mappings, we establish the local classical solvability of a problem for a hyperbolic system of quasilinear first-order equations with moving boundaries and nonlinear boundary conditions. Under additional assumptions on the monotonicity and sign constancy of initial data and a restriction on the growth of the right-hand sides of the system, we formulate sufficient conditions for the global classical solvability of the problem.

On the global continuous solvability of the mixed problem for one-dimensional hyperbolic systems of quasilinear equations

We consider a hyperbolic system of quasilinear equations written in Riemann invariants for the case of one spatial variable. For this system, we obtain sufficient conditions for the global generalized continuous solvability of the mixed problem in the class of functions monotone with respect to x for arbitrary t and with respect to t for x = 0. In contrast to earlier studies, we assume that the boundary conditions may depend not only on time but also on the unknown functions.

Generalized solutions of nonlinear differential equation and the maslov algebras of distributions

An associative commutative algebra including homogeneous and adjoint homogeneous distributions has been constructed. The products of distributions are continuous linear functionals. The conditions of solvability of strictly hyperbolic systems of quasilinear equations of the first order in the Maslov algebras are obtained.

The propagation of nonlinear waves in a bidisperse fluidized bed

A study is made of the propagation of nonlinear kinematic waves of concentrations of solid particles in a fluidized bed of particles of two different sizes. A hyperbolic system of quasilinear equations is obtained which describes the propagation of the waves. A dependence of the characteristic velocities on the concentrations of the phases and the ratio of the sizes of the particles is found. The influence of an admixture of fine particles on the propagation of porosity waves in the fluidized bed is analyzed. The nature of the formation of jumps in the porosity depending on the concentration of the admixture is studied, as is the process of the transfer of the admixture of fine particles in the bed. The nature of the propagation of nonlinear waves in a fluidized bed of identical particles is clarified. A characteristic velocity is found and conditions are determined for the formation of discontinuities of concentration of the dispserse phase in rarefaction compression waves.

Method of solution of certain boundary value problems for hyperbolic systems of quasilinear equations of first order with two variables: PMM vol. 39, n≗2, 1975, pp. 253–259

We propose a method of obtaining exact solutions of certain boundary value problems for hyperbolic systems of quasilinear equations of first order with two unknowns. The method utilizes special series. As an example, we solve the problem of motion of a plane, cylindrical or spherical piston in a gas with distributed density.

Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions

Solutions of the Riemann problem for hyperbolic systems of quasilinear equations without convexity conditions

Some geometric acoustic problems of one-dimensional unsteady and two-dimensional steady flows

The behavior of discontinuities (weak shocks) of the parameters of a disturbed flow and their interaction with the discontinuities of the basic flow in the geometric acoustics approximation, when the variation of the intensity of such shocks along the characteristics or the bicharacteristics is described by ordinary differential equations, has been investigated by many authors. Thus, Keller [1] considered the case when the undisturbed flow is three-dimensional and steady, and the external inputs do not depend on the flow parameters. An analogous study was made by Bazer and Fleischman for the MGD isentropic flow of an ideal conducting medium [2], while Lugovtsov [3] studied the three-dimensional steady flow of a gas of finite conductivity for small magnetic Reynolds numbers and no electric field. Several studies (for example, [4]) have considered the behavior of discontinuities of the solutions from the general positions of the theory of hyperbolic systems of quasilinear equations. Finally, the interaction of weak shocks (or the equivalent continuous disturbances) with shock waves was studied in [5–11].

Global solutions of certain hyperbolic systems of quasi-linear equations

Global solutions of certain hyperbolic systems of quasi-linear equations

Global continuous solutions of hyperbolic systems of quasi-linear equations

Global continuous solutions of hyperbolic systems of quasi-linear equations