-
Previous Article
Evolutionary dynamics of a multi-trait semelparous model
- DCDS-B Home
- This Issue
-
Next Article
Competition between two similar species in the unstirred chemostat
Destabilization threshold curves for diffusion systems with equal diffusivity under non-diagonal flux boundary conditions
1. | Graduate School of Science, Department of Mathematical and Life Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, 739-8526, Japan |
References:
[1] |
H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations, 72 (1988), 201-269.
doi: 10.1016/0022-0396(88)90156-8. |
[2] |
A. Anma and K. Sakamoto, Turing type mechanisms for linear diffusion systems under non-diagonal Robin boundary conditions, SIAM Journal on Mathematical Analysis, 45 (2013), 3611-3628.
doi: 10.1137/130908270. |
[3] |
J. M. Arrieta, A. N. Carvalho and A. Rodríguez-Bernal, Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions, J. Differential Equations, 168 (2000), 33-59.
doi: 10.1006/jdeq.2000.3876. |
[4] |
G. Auchmuty, Steklov eigenproblems and the representation of solutions of elliptic boundary value problems, Numerical Func. Anal. Opt., 25 (2004), 321-348.
doi: 10.1081/NFA-120039655. |
[5] |
H. Levine and W.-J. Rappel, Membrane-bound Turing patterns, Physical Review E, 72 (2005), 061912, 5pp.
doi: 10.1103/PhysRevE.72.061912. |
[6] |
J. D. Murray, Mathematical Biology, Biomathematics Texts, Springer-Verlag Berlin Heidelberg, 1989.
doi: 10.1007/978-3-662-08539-4. |
[7] |
Alan M. Turing, The chemical basis for morphogenesis, Phil. Trans. R. Soc. London, B 273 (1952), 37-72. |
[8] |
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1995. |
show all references
References:
[1] |
H. Amann, Parabolic evolution equations and nonlinear boundary conditions, J. Differential Equations, 72 (1988), 201-269.
doi: 10.1016/0022-0396(88)90156-8. |
[2] |
A. Anma and K. Sakamoto, Turing type mechanisms for linear diffusion systems under non-diagonal Robin boundary conditions, SIAM Journal on Mathematical Analysis, 45 (2013), 3611-3628.
doi: 10.1137/130908270. |
[3] |
J. M. Arrieta, A. N. Carvalho and A. Rodríguez-Bernal, Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions, J. Differential Equations, 168 (2000), 33-59.
doi: 10.1006/jdeq.2000.3876. |
[4] |
G. Auchmuty, Steklov eigenproblems and the representation of solutions of elliptic boundary value problems, Numerical Func. Anal. Opt., 25 (2004), 321-348.
doi: 10.1081/NFA-120039655. |
[5] |
H. Levine and W.-J. Rappel, Membrane-bound Turing patterns, Physical Review E, 72 (2005), 061912, 5pp.
doi: 10.1103/PhysRevE.72.061912. |
[6] |
J. D. Murray, Mathematical Biology, Biomathematics Texts, Springer-Verlag Berlin Heidelberg, 1989.
doi: 10.1007/978-3-662-08539-4. |
[7] |
Alan M. Turing, The chemical basis for morphogenesis, Phil. Trans. R. Soc. London, B 273 (1952), 37-72. |
[8] |
G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1995. |
[1] |
Ciprian G. Gal, Mahamadi Warma. Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. Discrete and Continuous Dynamical Systems, 2016, 36 (3) : 1279-1319. doi: 10.3934/dcds.2016.36.1279 |
[2] |
Ionuţ Munteanu. Boundary stabilization of non-diagonal systems by proportional feedback forms. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3113-3128. doi: 10.3934/cpaa.2021098 |
[3] |
Jihoon Lee, Vu Manh Toi. Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3135-3152. doi: 10.3934/dcdsb.2020054 |
[4] |
Narcisa Apreutesei, Vitaly Volpert. Reaction-diffusion waves with nonlinear boundary conditions. Networks and Heterogeneous Media, 2013, 8 (1) : 23-35. doi: 10.3934/nhm.2013.8.23 |
[5] |
José M. Arrieta, Simone M. Bruschi. Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 327-351. doi: 10.3934/dcdsb.2010.14.327 |
[6] |
Guangying Lv, Jinlong Wei, Guang-an Zou. Noise and stability in reaction-diffusion equations. Mathematical Control and Related Fields, 2022, 12 (1) : 147-168. doi: 10.3934/mcrf.2021005 |
[7] |
Zhao-Xing Yang, Guo-Bao Zhang, Ge Tian, Zhaosheng Feng. Stability of non-monotone non-critical traveling waves in discrete reaction-diffusion equations with time delay. Discrete and Continuous Dynamical Systems - S, 2017, 10 (3) : 581-603. doi: 10.3934/dcdss.2017029 |
[8] |
Abraham Solar. Stability of non-monotone and backward waves for delay non-local reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5799-5823. doi: 10.3934/dcds.2019255 |
[9] |
Marek Fila, Hirokazu Ninomiya, Juan-Luis Vázquez. Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 63-74. doi: 10.3934/dcds.2006.14.63 |
[10] |
Shin-Ichiro Ei, Toshio Ishimoto. Effect of boundary conditions on the dynamics of a pulse solution for reaction-diffusion systems. Networks and Heterogeneous Media, 2013, 8 (1) : 191-209. doi: 10.3934/nhm.2013.8.191 |
[11] |
Jihoon Lee, Nguyen Thanh Nguyen. Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation. Communications on Pure and Applied Analysis, 2021, 20 (3) : 1263-1296. doi: 10.3934/cpaa.2021020 |
[12] |
Cyrill B. Muratov, Xing Zhong. Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 915-944. doi: 10.3934/dcds.2017038 |
[13] |
Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications, 2009, 2009 (Special) : 526-535. doi: 10.3934/proc.2009.2009.526 |
[14] |
Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001 |
[15] |
Liang Zhang, Zhi-Cheng Wang. Threshold dynamics of a reaction-diffusion epidemic model with stage structure. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3797-3820. doi: 10.3934/dcdsb.2017191 |
[16] |
Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete and Continuous Dynamical Systems - B, 2021, 26 (9) : 4867-4885. doi: 10.3934/dcdsb.2020316 |
[17] |
Wenjing Wu, Tianli Jiang, Weiwei Liu, Jinliang Wang. Threshold dynamics of a reaction-diffusion cholera model with seasonality and nonlocal delay. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022099 |
[18] |
Thomas I. Seidman. Interface conditions for a singular reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2009, 2 (3) : 631-643. doi: 10.3934/dcdss.2009.2.631 |
[19] |
Alessio Fiscella, Enzo Vitillaro. Local Hadamard well--posedness and blow--up for reaction--diffusion equations with non--linear dynamical boundary conditions. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5015-5047. doi: 10.3934/dcds.2013.33.5015 |
[20] |
Costică Moroşanu, Bianca Satco. Qualitative and quantitative analysis for a nonlocal and nonlinear reaction-diffusion problem with in-homogeneous Neumann boundary conditions. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022042 |
2021 Impact Factor: 1.497
Tools
Metrics
Other articles
by authors
[Back to Top]