Quantum mechanics

Pure mathematics

Mathematical physics

Statistics

Energy (signal processing)

Physical chemistry

Thermodynamics

Physics

Nonlinear system

Diffusion

Mathematics

Combustion

Mathematical analysis

Uniqueness

Chemistry

SIAM Journal on Mathematical Analysis

The differential equation $y'' = y\exp (\alpha x - y)$, $\lim _{x \to - \infty } \frac{{dy}}{{dx}} = - \theta $ and $\lim _{x \to \infty } \frac{{dy}}{{dx}} = 0$ for $\theta > 0$ governs the thin reaction diffusion zone in many diverse problems in combustion theory. This problem with $\theta = 1$ is known as Liñán’s problem and continues to arise through the use of large activation energy asymptotics in the study of various combustion phenomena. The main issues for this problem are those of existence and uniqueness which we establish for each positive $\alpha $ and $\theta $.

A Nonlinear Problem Arising from Combustion Theory: Liñán’s Problem