Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

On a class of nonautonomous quasilinear systems with general time-gradually-degenerate damping

Richard De la cruz, Wladimir Neves

Abstract

In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and time-variable coefficient pressureless gas systems both with general time-gradually-degenerate damping. Applying the method of similar variables and nonlinear viscosity, we obtain classical Riemann solutions and delta shock wave solutions.

On a class of nonautonomous quasilinear systems with general time-gradually-degenerate damping

Abstract

In this paper, we study two systems with a time-variable coefficient and general time-gradually-degenerate damping. More explicitly, we construct the Riemann solutions to the time-variable coefficient Zeldovich approximation and time-variable coefficient pressureless gas systems both with general time-gradually-degenerate damping. Applying the method of similar variables and nonlinear viscosity, we obtain classical Riemann solutions and delta shock wave solutions.
Paper Structure (12 sections, 6 theorems, 126 equations)

This paper contains 12 sections, 6 theorems, 126 equations.

Table of Contents

  1. Introduction
  2. Equivalent $\times$ non-equivaqlent systems
  3. The Zeldovich Type Approximate System
  4. Parabolic regularization
  5. The Riemann problem
  6. Classical Riemann solutions: $u_- \le u_+$.
  7. Delta shock wave solutions: $u_- > u_+$.
  8. Pressureless Type Gas Dynamics System
  9. Classical Riemann solutions.
  10. Delta shock wave solutions.
  11. Riemann problem to the systems (4) and (5) with $\sigma(\cdot) \equiv 0$
  12. Comments and Extensions

Key Result

Proposition 2.1

Under the assumptions on the functions $\alpha, \beta, \sigma$, the explicit solution of the problem systemVis-DatRV is given by where and

Theorems & Definitions (15)

  • Proposition 2.1
  • proof
  • Remark 1
  • Theorem 2.1
  • proof
  • Definition 2.1
  • Definition 2.2
  • Theorem 2.2
  • proof
  • Proposition 3.1
  • ...and 5 more