非線性守恆律的廣域解(2/2)

Project Details

Description

In the first topic, we study the global classical solutions of the nozzle flow near vacuum in terms of the Riemann invariants for compressible Euler equations. We present the solutions for two kinds of variable nozzles. One is the C^2 expanding nozzle corresponding to the initial value problem of the nozzle flow. The other case is the piecewise C^2 nozzles, which is related to an initial-boundary value problem. These results are established by the application of the Lax-Li method. We first establish the local existence and then develop the uniform a prioriestimate to the first-order derivatives of the Riemann invariants. The former is from the local existence theorem in ODE. The latter is to study the solutions of the Riccati equations induced from Riemann invariants. These results imply the global C^1 solutions of the nozzle flow near vacuum. Theoretic results are also supported by numerical simulations. In this second topic, we consider a multilane model of traffic flow, which is governed by a hyperbolic system of conservation laws with a discontinuous relaxation term. Since the conservation laws forms a Temple class system which can help us to obtain the global entropy solution to the Cauchy problem of this multilane model by applying the generalized Glimm method. Then using the zero relaxation limit yields that the Cauchy problem forthe conservation law of mass (vehicles) with a discontinuous flux also admits a global weak solution.
StatusFinished
Effective start/end date1/08/2231/07/23

UN Sustainable Development Goals

In 2015, UN member states agreed to 17 global Sustainable Development Goals (SDGs) to end poverty, protect the planet and ensure prosperity for all. This project contributes towards the following SDG(s):

  • SDG 11 - Sustainable Cities and Communities
  • SDG 14 - Life Below Water
  • SDG 15 - Life on Land
  • SDG 17 - Partnerships for the Goals

Keywords

  • Compressible Euler equations
  • Nozzle flow
  • Vacuum
  • Hyperbolic systems of the conservation laws
  • Riemann invariants
  • A priori estimate
  • Riccati equations
  • Horizontally-separated lines
  • Aw-Rascle Model
  • Multilane model
  • Riemann problem
  • Shock waves
  • Rarefaction waves
  • Contact discontinuities
  • Temple class system
  • Zero relaxation limit

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