ScholarLens Back to search
1988•Quarterly of Applied MathematicsOpen access

A mathematical problem from detonation theory

Wildon Fickett

Open full text 4 citations

Abstract

A simplified abstraction of a partial-differential-equation problem which appears in the study of small perturbations on a detonation wave is studied. The interesting feature of this problem is that the function representing the unknown values of the dependent variable on one boundary appears as a source term in the partial differential equation. This unknown boundary function turns out to be the solution of an ordinary differential-difference equation. We study the properties of this differential-difference equation, and also present some representative solutions of the complete problem.

Open-access reader

About this research paper

What this paper is about

A simplified abstraction of a partial-differential-equation problem which appears in the study of small perturbations on a detonation wave is studied. The interesting feature of this problem is that the function representing the unknown values of the dependent variable on one boundary appears as a source term in the partial differential equation. This unknown boundary function turns out to be the solution of an ordinary differential-difference equation. We study the properties of this differential-difference equation, and also present some representative solutions of the complete problem.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A simplified abstraction of a partial-differential-equation problem which appears in the study of small perturbations on a detonation wave is studied. The interesting feature of this problem is that the function representing the unknown values of the dependent variable on one boundary appears as a source term in the partial differential equation. This unknown boundary function turns out to be the solution of an ordinary differential-difference equation. We study the properties of this differential-difference equation, and also present some representative solutions of the complete problem.

Key concepts: Partial differential equation, Mathematics, First-order partial differential equation, Ordinary differential equation, Boundary value problem, Differential equation, Detonation, Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
A mathematical problem from detonation theory — Research Paper | ScholarLens