Department of Mathematics and Statistics
Texas Tech University
1108 Memorial Circle
Lubbock, TX 79409-1042, USA
email: luan.hoang@ttu.edu
Luan Hoang
Abstract:
This article focuses on the behavior near the extinction time of
solutions to systems of ordinary differential equations with a
sublinear dissipation term. Suppose the dissipation term is a product
of a linear mapping \(A\) and a positively homogeneous scalar function
\(H\) of a negative degree \(-\alpha\). Then any solution with an extinction
time \(T_*\) behaves like \((T_*-t)^{1/\alpha}\xi_*\) as time \(t\to T_*^-\),
where \(\xi_*\) is an eigenvector of \(A\). The result allows the higher
order terms to be general and the nonlinear function \(H\) to take very
complicated forms. As a demonstration, our theoretical study is applied
to an inhomogeneous population model.
Submitted April 26, 2024. Published January 17, 2025.
Math Subject Classifications: 34D05, 41A60.
Key Words: Sublinear dissipation; extinction time; extinction profile;
vanish in finite time; asymptotic behavior; asymptotic approximation.
DOI: 10.58997/ejde.2025.08
Show me the PDF file (468 KB), TEX file for this article.
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Luan Hoang Department of Mathematics and Statistics Texas Tech University 1108 Memorial Circle Lubbock, TX 79409-1042, USA email: luan.hoang@ttu.edu |
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