• Corpus ID: 119328788

On some nonlinear evolution equation of second order

  title={On some nonlinear evolution equation of second order},
  author={Kamal N. Soltanov},
  journal={arXiv: Analysis of PDEs},
  • K. Soltanov
  • Published 3 December 2016
  • Mathematics
  • arXiv: Analysis of PDEs
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions and also investigate the behaviour of the solution. 



Nonlinear Functional Analysis And Its Applications

Resurrection of "Second Order" Models of Traffic Flow

A new "second order" model of traffic flow is introduced, which replaces the space derivative with a convective derivative and nicely predicts instabilities near the vacuum, i.e., for very light traffic.

Quelques méthodes de résolution de problèmes aux limites non linéaires

Coupling Conditions for a Class of Second-Order Models for Traffic Flow

This paper construction provides a solution of the Riemann problem at an arbitrary junction of a road network and provides the full system of conservation laws, in particular, all moments are conserved.

Flow on networks : recent results and prespectives , EMS Surveys in Math

  • Interpolation of operators , Pure and Applied Mathematics
  • 1988