Stability of the separable solutions for a nonlinear boundary diffusion problem
Tianling Jin, Jingang Xiong, Xuzhou Yang
TL;DR
This paper analyzes the stability and long-term behavior of solutions to a nonlinear boundary diffusion equation of porous medium type, providing a complete characterization of asymptotic behavior and stability of separable solutions.
Contribution
It offers a comprehensive and precise analysis of the asymptotic behavior and stability of separable solutions for a specific nonlinear boundary diffusion problem.
Findings
Complete characterization of asymptotic behavior
Proof of stability for separable solutions
Sharp conditions for solution stability
Abstract
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the stability of its separable solutions.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Differential Equations and Numerical Methods · Differential Equations and Boundary Problems