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Applicable Analysis
An International Journal
Volume 9, 1979 - Issue 2
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Original Articles

Bifurcation analysis on a nonlinear diffusion system in reactor dynamics

Pages 107-119 | Published online: 10 May 2007

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Qiang Tao & Hang Gao. (2020) On the null controllability of parabolic equations with nonlinear memory. International Journal of Control 93:7, pages 1745-1753.
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K. Sakthivel, K. Balachandran & B. R. Nagaraj. (2008) On a class of non-linear parabolic control systems with memory effects. International Journal of Control 81:5, pages 764-777.
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Articles from other publishers (33)

Chaoqun Li & Dongyang Shi. (2024) Low order nonconforming finite element methods for nuclear reactor model. Communications in Nonlinear Science and Numerical Simulation 133, pages 107900.
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Muhammad Abbas, Sadia Aslam, Farah Aini Abdullah, Muhammad Bilal Riaz & Khaled A. Gepreel. (2023) An efficient spline technique for solving time-fractional integro-differential equations. Heliyon 9:9, pages e19307.
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Ruipeng Chen, Jiayin Liu, Guangchen Zhang & Xiangyu Kong. (2021) Positive radial solutions for a noncooperative resonant nuclear reactor model with sign-changing nonlinearities. Journal of Inequalities and Applications 2021:1.
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Salwa A. Mohamed, Norhan A. Mohamed & Sarah I. Abo‐Hashem. (2021) A novel differential‐integral quadrature method for the solution of nonlinear integro‐differential equations. Mathematical Methods in the Applied Sciences 44:18, pages 13945-13967.
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Tayyaba Akram, Zeeshan Ali, Faranak Rabiei, Kamal Shah & Poom Kumam. (2021) A Numerical Study of Nonlinear Fractional Order Partial Integro-Differential Equation with a Weakly Singular Kernel. Fractal and Fractional 5:3, pages 85.
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Fairouz Tchier, Ioannis Dassios, Ferdous Tawfiq & Lakhdar Ragoub. (2021) On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions. Mathematics 9:3, pages 286.
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Kamil Khan, Arshed Ali, Fazal-i-Haq, Iltaf Hussain & Nudrat Amir. (2021) A Comparative Numerical Study of Parabolic Partial Integro-Differential Equation Arising from Convection-Diffusion. Computer Modeling in Engineering & Sciences 126:2, pages 673-692.
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Haniye Dehestani, Yadollah Ordokhani & Mohsen Razzaghi. (2020) The novel operational matrices based on 2D-Genocchi polynomials: solving a general class of variable-order fractional partial integro-differential equations. Computational and Applied Mathematics 39:4.
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Zhanwen Yang, Jiwei Zhang & Chengchao Zhao. (2019) Numerical blow-up analysis of linearly implicit Euler method for nonlinear parabolic integro-differential equations. Journal of Computational and Applied Mathematics 358, pages 343-358.
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Bhupen Deka & Ram Charan Deka. (2019) A priori $$\varvec{L^{\infty }(L^2)}$$ error estimates for finite element approximations to parabolic integro-differential equations with discontinuous coefficients. Proceedings - Mathematical Sciences 129:4.
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K. Harish Kumar & V. Antony Vijesh. (2018) Wavelet based iterative methods for a class of 2D-partial integro differential equations. Computers & Mathematics with Applications 75:1, pages 187-198.
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Farhad Fakhar-Izadi & Mehdi Dehghan. (2018) Fully spectral collocation method for nonlinear parabolic partial integro-differential equations. Applied Numerical Mathematics 123, pages 99-120.
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Zhanwen Yang, Tao Tang & Jiwei Zhang. (2017) Blowup of Volterra Integro-Differential Equations and Applications to Semi-Linear Volterra Diffusion Equations. Numerical Mathematics: Theory, Methods and Applications 10:4, pages 737-759.
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Yaser Rostami & Khosrow Maleknejad. (2017) Numerical Solution of Partial Integro-Differential Equations by using Projection Method. Mediterranean Journal of Mathematics 14:3.
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Ruipeng Chen & Xiaoya Li. (2016) The steady states of a non-cooperative model arising in reactor dynamics. Computers & Mathematics with Applications 72:3, pages 594-602.
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Qiang Tao & Zheng-An Yao. (2014) THE TIME OPTIMAL CONTROL OF PARABOLIC INTEGRODIFFERENTIAL EQUATION IN REACTOR DYNAMICS. Taiwanese Journal of Mathematics 18:2.
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Z. Avazzadeh, M. Heydari, W. Chen & G. B. Loghmani. (2014) SMOOTH SOLUTION OF PARTIAL INTEGRO-DIFFERENTIAL EQUATIONS USING RADIAL BASIS FUNCTIONS. Journal of Applied Analysis & Computation 4:2, pages 115-127.
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Ruipeng Chen & Ruyun Ma. (2013) Global bifurcation of positive radial solutions for an elliptic system in reactor dynamics. Computers & Mathematics with Applications 65:8, pages 1119-1128.
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Ruipeng Chen & Ruyun Ma. (2012) Positive solutions of the second-order differential systems in reactor dynamics. Applied Mathematics and Computation 219:8, pages 3882-3892.
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Z. Avazzadeh, Z. Beygi Rizi, F.M. Maalek Ghaini & G.B. Loghmani. (2012) A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions. Engineering Analysis with Boundary Elements 36:5, pages 881-893.
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Z. Avazzadeh, Z. Beygi Rizi, F. M. Maalek Ghaini & G. B. Loghmani. (2011) A semi-discrete scheme for solving nonlinear hyperbolic-type partial integro-differential equations using radial basis functions. Journal of Mathematical Physics 52:6.
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K. Sakthivel, K. Balachandran & S.S. Sritharan. (2008) Exact controllability of nonlinear diffusion equations arising in reactor dynamics. Nonlinear Analysis: Real World Applications 9:5, pages 2029-2054.
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H. Amann & P. Quittner. (2005) Optimal Control Problems with Final Observation Governed by Explosive Parabolic Equations. SIAM Journal on Control and Optimization 44:4, pages 1215-1238.
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Hongwei Chen. (1997) The dynamics of a nuclear reactor model. Nonlinear Analysis: Theory, Methods & Applications 30:6, pages 3409-3416.
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Hongwei Chen. (1997) Positive Steady-state Solutions of a Non-linear Reaction-Diffusion System. Mathematical Methods in the Applied Sciences 20:7, pages 625-634.
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B.G Pachpatte. (1983) On a nonlinear diffusion system arising in reactor dynamics. Journal of Mathematical Analysis and Applications 94:2, pages 501-508.
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C. V. Pao. (1983) Comparison and Stability of Solutions for a Neutron Transport Problem with Temperature Feedback. SIAM Journal on Mathematical Analysis 14:1, pages 167-184.
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C.V Pao. (1982) On nonlinear reaction-diffusion systems. Journal of Mathematical Analysis and Applications 87:1, pages 165-198.
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C. V. Pao & E. Meister. (2011) Stability and instability of the energy dependent diffusion system in reactor dynamics. Mathematical Methods in the Applied Sciences 3:1, pages 488-505.
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