Abstract
The system of Brusselator-type reaction-diffusion equations (RDs) on open bounded convex domains
References
[1] R. A. Adams and J. J. F. Fournier, Sobolev Spaces, 2nd ed., Pure Appl. Math. (Amsterdam) 140, Elsevier/Academic Press, Amsterdam, 2003. Search in Google Scholar
[2] L. Aharouch, M. Kbiri Alaoui, G. Di Fazio and M. Altanji, On a class of nonlinear elliptic problems with obstacle, Georgian Math. J. 28 (2021), no. 5, 665–675. 10.1515/gmj-2020-2085Search in Google Scholar
[3] G. A. Al-Juaifri and A. J. Harfash, Analysis of a nonlinear reaction-diffusion system of the Fitzhugh–Nagumo type with Robin boundary conditions, Ric. Mat. 72 (2023), no. 1, 335–357. 10.1007/s11587-022-00711-7Search in Google Scholar
[4] A. S. Al-Ofl, Analysis of complex nonlinear reaction-diffusion equations, Ph.D. thesis, Durham University, 2008. Search in Google Scholar
[5]
A. Ayoujil and A. Ourraoui,
On a Robin type problem involving
[6] F. Bahidi, B. Krichen and B. Mefteh, Existence results for a system of nonlinear operator equations and block operator matrices in locally convex spaces, Georgian Math. J. 29 (2022), no. 2, 179–192. 10.1515/gmj-2021-2127Search in Google Scholar
[7] R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology: Volume 2: Functional and Variational Methods, Springer, Berlin, 1999. Search in Google Scholar
[8] M. El Ouaarabi, C. Allalou and S. Melliani, On a class of nonlinear degenerate elliptic equations in weighted Sobolev spaces, Georgian Math. J. 30 (2023), no. 1, 81–94. 10.1515/gmj-2022-2191Search in Google Scholar
[9] L. C. Evans, Partial Differential Equations, Grad. Stud. Math. 19, American Mathematical Society, Providence, 1998. Search in Google Scholar
[10] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Monogr. Stud. Math. 24, Pitman, Boston, 1985. Search in Google Scholar
[11] P. Hartman, Ordinary Differential Equations, John Wiley & Sons, New York, 1964. Search in Google Scholar
[12] S. Heidari and A. Razani, Infinitely many solutions for nonlocal elliptic systems in Orlicz–Sobolev spaces, Georgian Math. J. 29 (2022), no. 1, 45–54. 10.1515/gmj-2021-2110Search in Google Scholar
[13] S. Heidarkhani, G. Caristi, G. A. Afrouzi and S. Moradi, Existence results for a non-homogeneous Neumann problem through Orlicz–Sobolev spaces, Georgian Math. J. 28 (2021), no. 2, 241–253. 10.1515/gmj-2019-2054Search in Google Scholar
[14] S. Heidarkhani, G. Caristi and M. Ferrara, Perturbed Kirchhoff-type Neumann problems in Orlicz–Sobolev spaces, Comput. Math. Appl. 71 (2016), no. 10, 2008–2019. 10.1016/j.camwa.2016.03.019Search in Google Scholar
[15]
S. Heidarkhani, A. Ghobadi and M. Avci,
Multiple solutions for a class of
[16]
S. Heidarkhani, S. Moradi and M. Avci,
Critical points approaches to a nonlocal elliptic problem driven by
[17] R. M. Jena, S. Chakraverty, H. Rezazadeh and D. Domiri Ganji, On the solution of time-fractional dynamical model of Brusselator reaction-diffusion system arising in chemical reactions, Math. Methods Appl. Sci. 43 (2020), no. 7, 3903–3913. 10.1002/mma.6141Search in Google Scholar
[18] R. Kamocki, On generalized fractional integration by parts formulas and their applications to boundary value problems, Georgian Math. J. 28 (2021), no. 1, 99–108. 10.1515/gmj-2019-2006Search in Google Scholar
[19] S. Kharibegashvili and B. Midodashvili, The boundary value problem for one class of higher-order nonlinear partial differential equations, Georgian Math. J. 29 (2022), no. 3, 387–395. 10.1515/gmj-2021-2139Search in Google Scholar
[20] Y. Li, Hopf bifurcations in general systems of Brusselator type, Nonlinear Anal. Real World Appl. 28 (2016), 32–47. 10.1016/j.nonrwa.2015.09.004Search in Google Scholar
[21]
F.-F. Liao, S. Heidarkhani and S. Moradi,
Multiple solutions for nonlocal elliptic problems driven by
[22] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969. Search in Google Scholar
[23]
D. T. Luyen and L. T. H. Hanh,
Infinitely many solutions for perturbed
[24] M. Makvand Chaharlang and A. Razani, Two weak solutions for some Kirchhoff-type problem with Neumann boundary condition, Georgian Math. J. 28 (2021), no. 3, 429–438. 10.1515/gmj-2019-2077Search in Google Scholar
[25] M. Naceri, Anisotropic nonlinear weighted elliptic equations with variable exponents, Georgian Math. J. 30 (2023), no. 2, 277–285. 10.1515/gmj-2022-2216Search in Google Scholar
[26] D. Natroshvili and T. Tsertsvadze, On an alternative approach for mixed boundary value problems for the Laplace equation, Georgian Math. J. 29 (2022), no. 6, 883–895. 10.1515/gmj-2022-2177Search in Google Scholar
[27] I. Prigogine and R. Lefever, Symmetry breaking instabilities in dissipative systems. II, J. Chem. Phys. 48 (1968), no. 4, 1695–1700. 10.1063/1.1668896Search in Google Scholar
[28] I. Prigogine and G. Nicolis, Self-organisation in nonequilibrium systems: Towards a dynamics of complexity, Bifurcation Analysis, Reidel, Dordrecht (1985), 3–12. 10.1007/978-94-009-6239-2_1Search in Google Scholar
[29] P. C. Rech, Nonlinear dynamics of two discrete-time versions of the continuous-time Brusselator model, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 29 (2019), no. 10, Article ID 1950142. 10.1142/S0218127419501426Search in Google Scholar
[30] J. C. Robinson, Infinite-Dimensional Dynamical Systems, Cambridge Texts Appl. Math., Cambridge University, Cambridge, 2001. Search in Google Scholar
[31] J. C. Robinson, Infinite-Dimensional Dynamical Systems. An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts Appl. Math., Cambridge University, Cambridge, 2001. Search in Google Scholar
[32] J. A. Sherratt, A comparison of periodic travelling wave generation by Robin and Dirichlet boundary conditions in oscillatory reaction-diffusion equations, IMA J. Appl. Math. 73 (2008), no. 5, 759–781. 10.1093/imamat/hxn015Search in Google Scholar
[33] J. J. Tyson, Some further studies of nonlinear oscillations in chemical systems, J. Chem. Phys. 58 (1973), no. 9, 3919–3930. 10.1063/1.1679748Search in Google Scholar
[34] A. Ženíšek, Nonlinear Elliptic and Evolution Problems and Their Finite Element Approximations, Comput. Math. Appl., Academic Press, London, 1990. Search in Google Scholar
[35] T. L. Żynda, J. J. Sadowski, P. M. Wójcicki and S. G. Krantz, Reproducing kernels and minimal solutions of elliptic equations, Georgian Math. J. 30 (2023), no. 2, 303–320. 10.1515/gmj-2022-2202Search in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions
- Generalized Euclidean operator radius
- New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions
- Characterization of Hilbert C*-module higher derivations
- On the standing wave in coupled fractional Klein–Gordon equation
- Fractal Mellin transform and non-local derivatives
- On 〈s〉-generalized topologies
- Study on discrete degenerate Bell distributions with two parameters
- Multi-dimensional almost automorphic type sequences and applications
- The second nonlinear mixed Lie triple derivations on standard operator algebras
- On geometrical characteristics and inequalities of new bicomplex Lebesgue Spaces with hyperbolic-valued norm
- Bilinear multipliers on weighted Orlicz spaces
- Estimates for the commutators of Riesz transforms related to Schrödinger-type operators
- Reproducing kernel Banach space defined by the minimal norm property and applications to partial differential equation theory
Articles in the same Issue
- Frontmatter
- Existence and uniqueness of solution for the nonlinear Brusselator system with Robin boundary conditions
- Generalized Euclidean operator radius
- New quantum integral inequalities for left and right log-ℏ-convex interval-valued functions
- Characterization of Hilbert C*-module higher derivations
- On the standing wave in coupled fractional Klein–Gordon equation
- Fractal Mellin transform and non-local derivatives
- On 〈s〉-generalized topologies
- Study on discrete degenerate Bell distributions with two parameters
- Multi-dimensional almost automorphic type sequences and applications
- The second nonlinear mixed Lie triple derivations on standard operator algebras
- On geometrical characteristics and inequalities of new bicomplex Lebesgue Spaces with hyperbolic-valued norm
- Bilinear multipliers on weighted Orlicz spaces
- Estimates for the commutators of Riesz transforms related to Schrödinger-type operators
- Reproducing kernel Banach space defined by the minimal norm property and applications to partial differential equation theory