Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity

Ayşe Fidan; Erhan Pişkin

Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity

Abstract

In this work, we obtain a singular parabolic m-biharmonic equation with logarithmic nonlinearity. We establish the decay of the solutions and then derive it using the potential well method and the Hardy-Sobolev inequality.

Keywords

References

Adams, R. A. & Fournier, J. J. F. (2003). Sobolev Spaces, Academic Press, New York.
Deng, X. & Zhou, J. (2020). Global existence and blow-up of solutions to a semilinear heat equation with singular potential and logarithmic nonlinearity, Communications on Pure and Applied Analysis, 19(2), 923-939.
Pişkin, E. & Okutmuştur, B. (2021). An introduction to Sobolev spaces, Bentham Science Publishers.
Fidan, A., Pişkin, E. & Çelik, E. (2024). Existence, Decay, and Blow-up of Solutions for a Weighted m-Biharmonic Equation with Nonlinear Damping and Source Terms, Journal of Function Spaces, 2024(1), 5866792.
Freitas, P. & Zuazua, E. (1996). Stability results for the wave equation with indefinite damping, J. Differential Equations, 132(2), 338-352.
Al-Gharabli, M. M. & Al-Mahdi, M. (2022). Existence and stability results of a plate equation with nonlinear damping and source term, Electronic Research Archive, 30(11), 4038-4065.
Han, Y. (2022). Blow-up phenomena for a reaction diffusion equation with special diffusion process, Applicable Analysis, 101(6), 1971-1983.
Han, Y. (2021). Blow-up phenomena for a fourth-order parabolic equation with a general nonlinearity, Journal of Dynamical and Control Systems, 27, 261-270.

Komornik, V. (1994). Exact Controllability and Stabilization, The Multiplier Method, Research in Applied Mathematics, Masson-John Wiley, Paris.
Lazer, A. C. & McKenna, P. J. (1990). Large-amplitude periodic oscillations in suspension bridges: Some new connections with nonlinear analysis, SIAM Rev., 32(4), 537-578.
Le, C. N. & Le, X. T. (2017). Global solution and blow-up for a class of p-Laplacian evolution equations with logarithmic nonlinearity, Acta Applicandae Mathematicae, 151(1), 149-169.
Liu, Z. & Fang, Z. B. (2023). On a singular parabolic p-biharmonic equation with logarithmic nonlinearity, Nonlinear Analysis: Real World Applications, 70, 103780.
Nachman, A. & Callegari, A. (1980). A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math., 38(2), 275-281.
Ortiz, M., Repetto, E. & Si, A. H. (1999). A continuum model of kinetic roughening and coarsening in thin films, J. Mech. Phys. Solids, 47, 697-730.
Pişkin, E. & Fidan, A. (2022). Nonexistence of global solutions for the strongly damped wave equation with variable coefficients, Universal Journal of Mathematics and Applications, 5(2), 51-56.
Pişkin, E. & Fidan, A. (2023). Finite time blow up of solutions for the m-Laplacian equation with variable coefficients, Al-Qadisiyah Journal of Pure Science, 28:1.
Thanh, B. L. T., Trong, N. N. & Do, T. D. (2021). Blow-up estimates for a higher-order reaction-diffusion equation with a special diffusion process, Journal of Elliptic and Parabolic Equations, 7, 891-904.
Thanh, B. L. T., Trong, N. N. & Do, T. D. (2023). Bounds on blow-up time for a higher-order non-Newtonian filtration equation, Mathematica Slovaca, 73(3), 749-760.
Wu, X., Zhao, Y. & Yang, X. (2023). Global existence and blow-up of solution to a class of fourth-order equation with singular potential and logarithmic nonlinearity, Electronic Journal of Qualitative Theory of Differential Equations, (55), 1-16.
Wu, X., Zhao, Y. & Yang, X. (2024). On a singular parabolic p-Laplacian equation with logarithmic nonlinearity, Commun. Anal. Mech., 16, 528-553.
Yang, H. (2024). A new blow-up criterion for a p-Laplacian type pseudo-parabolic equation with singular potential and logarithmic nonlinearity, Research Square, 48(8), 2489-2501.

Details

Primary Language

English

Subjects

Partial Differential Equations

Journal Section

Research Article

Authors

Ayşe Fidan ^*
0000-0001-6988-8333
Türkiye

Erhan Pişkin
0000-0001-6587-4479
Türkiye

Publication Date

December 31, 2024

Submission Date

December 19, 2024

Acceptance Date

December 27, 2024

Published in Issue

Year 2024 Volume: 1 Number: 1

IZ

https://izlik.org/JA99WP68JH

Cite

RIS / Bibtex

APA

Fidan, A., & Pişkin, E. (2024). Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity. Türkiye Mathematical Sciences, 1(1), 28-38. https://izlik.org/JA99WP68JH

AMA

1.Fidan A, Pişkin E. Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity. TMS. 2024;1(1):28-38. https://izlik.org/JA99WP68JH

Chicago

Fidan, Ayşe, and Erhan Pişkin. 2024. “Decay of Solutions for a Singular Parabolic M-Biharmonic Equation With Logarithmic Nonlinearity”. Türkiye Mathematical Sciences 1 (1): 28-38. https://izlik.org/JA99WP68JH.

EndNote

Fidan A, Pişkin E (December 1, 2024) Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity. Türkiye Mathematical Sciences 1 1 28–38.

IEEE

[1]A. Fidan and E. Pişkin, “Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity”, TMS, vol. 1, no. 1, pp. 28–38, Dec. 2024, [Online]. Available: https://izlik.org/JA99WP68JH

ISNAD

Fidan, Ayşe - Pişkin, Erhan. “Decay of Solutions for a Singular Parabolic M-Biharmonic Equation With Logarithmic Nonlinearity”. Türkiye Mathematical Sciences 1/1 (December 1, 2024): 28-38. https://izlik.org/JA99WP68JH.

JAMA

1.Fidan A, Pişkin E. Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity. TMS. 2024;1:28–38.

MLA

Fidan, Ayşe, and Erhan Pişkin. “Decay of Solutions for a Singular Parabolic M-Biharmonic Equation With Logarithmic Nonlinearity”. Türkiye Mathematical Sciences, vol. 1, no. 1, Dec. 2024, pp. 28-38, https://izlik.org/JA99WP68JH.

Vancouver

1.Ayşe Fidan, Erhan Pişkin. Decay of solutions for a singular parabolic m-biharmonic equation with logarithmic nonlinearity. TMS [Internet]. 2024 Dec. 1;1(1):28-3. Available from: https://izlik.org/JA99WP68JH