Existence of Classic Solution of the Boussinesq Equation

TL;DR

This paper extends the intermediate value theorem to metric spaces and uses this generalization to establish the existence of classical solutions for the Boussinesq equation.

Contribution

It introduces a novel generalization of the intermediate value theorem to metric spaces and applies it to prove solution existence for the Boussinesq equation.

Findings

Established the existence of classical solutions under new conditions

Generalized intermediate value theorem to metric spaces

Provided a framework for analyzing PDE solutions

Abstract

We generalize intermediate value Theorem to metric space,and make use of it to discuss existence of classic solution of the Boussinesq equation.