Upper and lower blow-up rate estimates of a semilinear heat equation with a nonlinear boundary condition
*Maan A. RasheedCorresponding authormaan.rasheed.edbs@uomustansiriyah.edu.iqDepartment of MathematicsCollege of Basic EducationBaghdad 10054Mustansiriyah UniversityIraqView full profile → , Miroslav ChlebikM.Chlebik@sussex.ac.ukDepartment of MathematicsSchool of Mathematical and Physical SciencesBrighton BN1 9RH, U. KUniversity of SussexView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Mar 2021
- Published Online:
- 01 Mar 2023
- Article type:
- A
- Language:
- EN
- Article no.:
- JIM-1302
- Pages:
- 163–175
Abstract
Keywords
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References
[1] P. Quittner and Ph. Souplet, Superlinear Parabolic Problems. Blow-up, Global Existence and Steady States, Birkhuser Advanced Texts, Birkhuser, Basel, (2007).
[2] M. A. Rasheed, H. A. S. Al-Dujaly, T. J. Aldhlki, Blow-up rate estimates for a system of reaction-diffusion equations with gradient terms, International Journal of Mathematics and Mathematical Sciences, 2019(1) 1-7 ; (2019).
[3] M. A. Rasheed and L. J. Barghooth, Blow-up set and upper rate estimate for a semilinear heat equation, Journal of Physics: Conf. Series 1294(2019) 032013.
[4] M. A. Rasheed, Deriving the upper blow-up rate estimate for a parabolic problem, Iraqi Journal of Science, special issue, The first conference of Mathematics, (2020), 200-203.
[5] M. A. Rasheed and M. Chlebik, blow-up rate estimates and blow-up set for a system of two heat equations with coupled nonlinear Neumann boundary conditions, Iraqi journal of Science, 61(1) , 147-152, (2020).
[6] M. A. Rasheed, R. A. Hameed, S. K. Obeid, A. F. Jameel, On numerical blow-up solutions of semilinear heat equations, Iraqi Journal of Science, 61(8), 2077-2086, (2020).
[7] M. A. Rasheed, On blow-up solutions of a parabolic system coupled in both equations and boundary conditions, Baghdad Science Journal, 18(2), 315-321, (2021).
[8] M. Chipot, M. Fila and P. Quittner, Stationary solutions, blow-up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions, Acta Math. Univ. Comenian. 60, 35-103, (1991).
[9] J. D. Rossi, The blow-up rate for a semilinear parabolic equation with a nonlinear boundary condition, Acta Math. Univ. Comenian. 67, 343-350, (1998).
[10] Z. Lin and M. Wang, The blow-up properties of solutions to semilinear heat equations with nonlinear boundary conditions, Z. Angew. Math. Phys. 50, 361-374, (1999).
[11] S. N. Zheng, F. J. Li and B. C. Liu, Asymptotic behavior for a reaction-diffusion equation with inner absorption and boundary flux, Appl. Math. Lett. 19, 942-948, (2006).
[12] K. Deng, The blow-up behavior of the heat equation with Neumann boundary conditions, J. Math. Anal. Appl. 188, 641-650, (1994).
[13] O. A. Ladyzenskaja, V.A.Solonnikov and N.N.Uralceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, American Mathematical Society, 23, (1968).
[14] C. V. Pao., Nonlinear Parabolic and Elliptic Equations, New York and London: Plenum Press, (1992).
[15] A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N.J., (1964).




