The class of second order quasilinear equations: models, solutions and background of classification

TL;DR

This paper investigates unsteady solutions of specific quasilinear hyperbolic models, introduces peculiar solutions, and develops a classification scheme for second order quasilinear equations based on these models.

Contribution

It presents a new classification framework for second order quasilinear equations derived from models with unique solutions.

Findings

Identification of peculiar solutions in quasilinear hyperbolic models

Development of a classification scheme for second order quasilinear equations

Insights into the behavior of solutions in mutually penetrating continua

Abstract

The paper is concerned with the unsteady solutions to the model of mutually penetrating continua and quasilinear hyperbolic modification of the Burgers equation (QHMB). The studies were focused on the peculiar solutions of models in question. On the base of these models and their solutions, the ideas of second order quasilinear models classification were developed.