Asymptotic behavior of a quasilinear parabolic equation in a band domain with unbounded boundary slopes
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- by Lixia Yuan;
- Proc. Amer. Math. Soc. 153 (2025), 2481-2489
- DOI: https://doi.org/10.1090/proc/17222
- Published electronically: April 3, 2025
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Abstract:
In this paper we consider a quasilinear parabolic equation in a band domain with Robin boundary conditions. The equation arises from the heat equation and some curvature flows. We will show that the equation has three types of translating solutions according to the form of the equation: the first type has a power-function-like profile, the second type has a Grim Reaper-like profile, and the third type has a cup-like profile. We then show that the solution $u$ of the initial-boundary value problem tends to infinite as $t\to \infty$, and $u(x,t)-u(0,t)$ tends to vertical line in the first type case, and tends to the corresponding translating solutions in the second and third type cases.References
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Bibliographic Information
- Lixia Yuan
- Affiliation: Mathematics and Science College, Shanghai Normal University, Shanghai 200234, People’s Republic of China
- Email: yuanlixia@shnu.edu.cn
- Received by editor(s): February 27, 2024
- Received by editor(s) in revised form: June 22, 2024, and August 20, 2024
- Published electronically: April 3, 2025
- Additional Notes: The author was supported by the National Natural Science Foundation of China (12001375).
- Communicated by: Wenxian Shen
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 153 (2025), 2481-2489
- MSC (2020): Primary 35K93, 35C07
- DOI: https://doi.org/10.1090/proc/17222
- MathSciNet review: 4892621