Existence and uniqueness of classical solution to an initial-boundary value problem for the unsteady general planar Broadwell model with four velocities

TL;DR

This paper proves the existence and uniqueness of a classical solution for the unsteady planar Broadwell model with four velocities, given bounded, continuous initial and boundary data with their derivatives.

Contribution

It establishes the first rigorous proof of existence and uniqueness for solutions to this specific initial-boundary value problem in the Broadwell model.

Findings

Existence of a unique classical solution is proven.

Solution remains bounded and continuous with derivatives.

Applicable to a class of bounded, continuous initial and boundary data.

Abstract

We consider the unsteady problem for the general planar Broadwell model with four velocities in a rectangular spatial domain over a finite time interval. We impose a class of non-negative initial and Dirichlet boundary data that are bounded and continuous, along with their first-order partial derivatives. We then prove the existence and uniqueness of a non-negative continuous solution, bounded together with its first-order partial derivatives, to the initial-boundary value problem.