On some nonlinear evolution equation of second order

TL;DR

This paper investigates a second-order nonlinear differential equation, including special cases related to traffic flow, proving solvability and analyzing solution behavior under certain conditions.

Contribution

It introduces a solvability theorem for a class of second-order nonlinear equations and explores their solution behavior, extending understanding of such equations.

Findings

Proved solvability under specific conditions

Analyzed the behavior of solutions

Connected the equation to traffic flow models

Abstract

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.