Spatial properties of transient heat equations on two types of special cylinders

Yuanfei Li; Yuanfei Li

doi:10.3934/era.2026380

Electronic Research Archive

2026, Volume 34, Issue 12: 9033-9045. doi: 10.3934/era.2026380

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Spatial properties of transient heat equations on two types of special cylinders

Yuanfei Li ^,

Institute of Digital Technology and Application, Guangzhou Huashang College, Guangdong 511300, China

Received: 26 June 2026 Revised: 02 September 2026 Accepted: 14 September 2026 Published: 26 October 2026

This paper investigates spatial properties of transient heat equations on two special cylinders under non-homogeneous boundary conditions. By introducing a key cross-sectional parameter, the author reveals how the cylinder's geometry affects the asymptotic behavior of solutions. Furthermore, spatial growth and decay rates are derived for different parameter ranges.
- transient heat equations,
- cross-sectional parameter,
- continuous dependence,
- asymptotic behavior
Citation: Yuanfei Li. Spatial properties of transient heat equations on two types of special cylinders[J]. Electronic Research Archive, 2026, 34(12): 9033-9045. doi: 10.3934/era.2026380

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Abstract

This paper investigates spatial properties of transient heat equations on two special cylinders under non-homogeneous boundary conditions. By introducing a key cross-sectional parameter, the author reveals how the cylinder's geometry affects the asymptotic behavior of solutions. Furthermore, spatial growth and decay rates are derived for different parameter ranges.

References

[1]	W. T. Huo, Z. B. Fang, Global existence and nonexistence for an inhomogeneous quasilinear convection-diffusion equation, Math. Nachr., 298 (2025), 3515–3539. https://doi.org/10.1002/mana.70056 doi: 10.1002/mana.70056
[2]	R. Molinarolo, Existence result for a nonlinear mixed boundary value problem for the heat equation, J. Math. Anal. Appl., 543 (2025), 128878. https://doi.org/10.1016/j.jmaa.2024.128878 doi: 10.1016/j.jmaa.2024.128878
[3]	C. O. Alves, T. Boudjeriou, H. Prado, Existence of solution and qualitative behavior for a class of heat equations, J. Differ. Equations, 400 (2024), 457–486. https://doi.org/10.1016/j.jde.2024.04.019 doi: 10.1016/j.jde.2024.04.019
[4]	L. E. Payne, G. A. Philippin, S. V. Piro, Blow-up phenomena for a semilinear heat equation with nonlinear boundary condition, II, Nonlinear Anal., 73 (2010), 971–978. https://doi.org/10.1016/j.na.2010.04.023 doi: 10.1016/j.na.2010.04.023
[5]	L. E. Payne, P. W. Schaefer, Lower bound for blow-up time in parabolic problems under Dirichlet conditions, Appl. Anal., 85 (2006), 1301–1311. https://doi.org/10.1080/00036810600915730 doi: 10.1080/00036810600915730
[6]	Y. F. Li, Y. Liu, C. H. Lin, Blow-up phenomena for some nonlinear parabolic problem under mixed conditions, Nonlinear Anal. Real World Appl., 11 (2010), 3815–3823. https://doi.org/10.1016/j.nonrwa.2010.02.011 doi: 10.1016/j.nonrwa.2010.02.011
[7]	W. Chen, R. Ikehata, Some remarks on large-time behaviors for the linearized compressible Navier-Stokes equations, Differ. Integr. Equations, 37 (2024), 699–716. https://doi.org/10.57262/die037-0910-699 doi: 10.57262/die037-0910-699
[8]	Y. Liu, X. L. Qin, S. H. Zhang, Global existence and estimates for Blackstock's model of thermoviscous flow with second sound phenomena, J. Differ. Equations, 324 (2022), 76–101. https://doi.org/10.1016/j.jde.2022.04.001 doi: 10.1016/j.jde.2022.04.001
[9]	J. Taler, P. Duda, Solving Direct and Inverse Heat Conduction Problems, Springer Berlin Heidelberg, 2006.
[10]	C. O. Horgan, L. E. Payne, L. T. Wheeler, Spatial decay estimates in transient heat conduction, Q. Appl. Math., 42 (1984), 119–127. https://doi.org/10.1090/qam/736512 doi: 10.1090/qam/736512
[11]	Y. F. Li, X. J. Chen, J. C. Shi, Phragmén-Lindelöf alternative for the heat conduction equations in a binary mixture, J. Shandong Univ., 55 (2020), 1–12.
[12]	R. Quintanilla, Some remarks on the fast spatial growth/decay in exterior regions, Z. Angew. Math. Phys., 70 (2019), 83. https://doi.org/10.1007/s00033-019-1127-x doi: 10.1007/s00033-019-1127-x
[13]	R. J. Knops, R. Quintanilla, Spatial decay in transient heat conduction for general elongated regions, Q. Appl. Math., 76 (2018), 611–625. https://doi.org/10.1090/qam/1497 doi: 10.1090/qam/1497
[14]	J. C. Shi, Spatial decay estimates for the Moore-Gibson-Thompson Heat equation, Wuhan Univ. J. Nat. Sci., 29 (2024), 397–402. https://doi.org/10.1051/wujns/2024295397 doi: 10.1051/wujns/2024295397
[15]	J. R. Fernández, R. Quintanilla, Spatial-time decay for nonlinear problems backward in time, Nonlinear Differ. Equations Appl., 32 (2025), 10. https://doi.org/10.1007/s00030-024-01010-w doi: 10.1007/s00030-024-01010-w
[16]	J. R. Fernández, R. Quintanilla, Spatio-temporal decay estimates for third order parabolic backward in time PDE, Ric. Mat., 74 (2025), 2117–2125. https://doi.org/10.1007/s11587-025-00940-6 doi: 10.1007/s11587-025-00940-6
[17]	W. Chen, H. Takeda, Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case, Nonlinear Anal., 234 (2023), 113316. https://doi.org/10.1016/j.na.2023.113316 doi: 10.1016/j.na.2023.113316
[18]	T. Liu, B. L. Ding, A radial basis function neural network approach for solving a diffusion partial differential equation efficiently, Appl. Math. Comput., 509 (2026), 129651. https://doi.org/10.1016/j.amc.2025.129651 doi: 10.1016/j.amc.2025.129651
[19]	T. Liu, R. Q. Xue, A convergent multi-step efficient iteration method to solve nonlinear equation systems, J. Appl. Math. Comput., 71 (2025), 2571–2588. https://doi.org/10.1007/s12190-024-02324-9 doi: 10.1007/s12190-024-02324-9
[20]	F. Y. Li, J. C. Shi, P. Zeng, Phragmén-Lindelöf alternative type results for the harmonic equation in a 3D cylinder, Nat. Sci. J. Hainan Univ., 38 (2020), 6–12. https://doi.org/10.15886/j.cnki.hdxbzkb.2020.0002 doi: 10.15886/j.cnki.hdxbzkb.2020.0002

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