Model problems for two equations, which type depends on solution

TL;DR

This paper investigates model problems for two nonlinear equations, including a nonlinear analog of the Lavrent'ev-Bitsadze equation, where the type of the equations depends on their solutions.

Contribution

It introduces a new class of model problems for nonlinear equations with solution-dependent types, expanding understanding of such equations.

Findings

Characterization of solution-dependent equation types

Development of model problems for nonlinear equations

Insights into the behavior of nonlinear analogs of Lavrent'ev-Bitsadze equation

Abstract

In this work there are considered model problems for two nonlinear equations, which type depends on the solution. One of the equations may be called a nonlinear analog of the Lavrent'ev-Bitsadze equation.