-
Previous Article
Oscillatory dynamics in a reaction-diffusion system in the presence of 0:1:2 resonance
- NHM Home
- This Issue
-
Next Article
Self-similar solutions in a sector for a quasilinear parabolic equation
Periodically growing solutions in a class of strongly monotone semiflows
1. | Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa, Ishikawa 920-1192, Japan |
2. | Department of Mathematics, Josai University, 1-1, Keyakidai, Sakado, Saitama 350-0295, Japan |
References:
[1] |
Y. Giga, N. Ishimura and Y. Kohsaka, Spiral solutions for a weakly anisotropic curvature flow equation, Adv. Math. Sci. Appl., 12 (2002), 393-408. |
[2] |
M. W. Hirsch, Differential equations and convergence almost everywhere in strongly monotone semiflows, in "Nonlinear Partial Differential Equations" (ed. N. H. Durham), (1982), 267-285, Contemp. Math., 17, Amer. Math. Soc., Providence, R.I., (1983). |
[3] |
M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 383 (1988), 1-53.
doi: 10.1515/crll.1988.383.1. |
[4] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Providence, R. I., 1967. |
[5] |
A. Lunardi, Abstract quasilinear parabolic equations, Math. Annalen, 267 (1984), 395-415.
doi: 10.1007/BF01456097. |
[6] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhäuser Verlag, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[7] |
H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ., 18 (1978), 221-227. |
[8] |
H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Tokyo, 30 (1984), 645-673. |
[9] |
H. Matano, Strongly order-preserving local semi-dynamical systems - theory and applications, in "Semigroups, Theory and Applications" I, Pitman Res. Notes Math. Ser., 141, Longman Sci. Tech., Harlow, (1986). |
[10] |
H. Matano, Asymptotic behavior of solutions of semilinear heat equations on $S^1$, in "Nonlinear Diffusion Equations and Their Equilibrium States" II ( eds. W.-M. Ni, L. A. Peletier and J. Serrin), Math. Sci. Res. Inst. Publ., 13, Springer, (1988), 139-162.
doi: 10.1007/978-1-4613-9608-6_8. |
[11] |
H. Matano, K. -I. Nakamura and B. Lou, Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit, Netw. Heterog. Media, 1 (2006), 537-568.
doi: 10.3934/nhm.2006.1.537. |
[12] |
G. Namah and J.-M. Roquejoffre, Convergence to periodic fronts in a class of semilinear parabolic equations, NoDEA Nonlinear Differential Equations Appl., 4 (1997), 521-536.
doi: 10.1007/s000300050029. |
[13] |
T. Ogiwara and H. Matano, Monotonicity and convergence results in order-preserving systems in the presence of symmetry, Discrete Contin. Dynam. Systems, 5 (1999), 1-34. |
[14] |
T. Ogiwara and K.-I. Nakamura, Spiral traveling wave solutions of nonlinear diffusion equation related to a model of spiral crystal growth, Publ. Res. Inst. Math. Sci., 39 (2003), 767-783. |
[15] |
P. Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations, 79 (1989), 89-110.
doi: 10.1016/0022-0396(89)90115-0. |
[16] |
H. L. Smith and H. R. Thieme, Quasi convergence and stability for strongly order-preserving semiflows, SIAM J. Math. Anal., 21 (1990), 673-692.
doi: 10.1137/0521036. |
[17] |
H. L. Smith and H. R. Thieme, Convergence for strongly order-preserving semiflows, SIAM J. Math. Anal., 22 (1991), 1081-1101.
doi: 10.1137/0522070. |
[18] |
T. I. Zelenyak, Stabilisation of solution of boundary value problems for a second-order equation with one space variable, Differ. Equations, 4 (1968), 17-22. |
show all references
References:
[1] |
Y. Giga, N. Ishimura and Y. Kohsaka, Spiral solutions for a weakly anisotropic curvature flow equation, Adv. Math. Sci. Appl., 12 (2002), 393-408. |
[2] |
M. W. Hirsch, Differential equations and convergence almost everywhere in strongly monotone semiflows, in "Nonlinear Partial Differential Equations" (ed. N. H. Durham), (1982), 267-285, Contemp. Math., 17, Amer. Math. Soc., Providence, R.I., (1983). |
[3] |
M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems, J. Reine Angew. Math., 383 (1988), 1-53.
doi: 10.1515/crll.1988.383.1. |
[4] |
O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, "Linear and Quasilinear Equations of Parabolic Type," Amer. Math. Soc., Providence, R. I., 1967. |
[5] |
A. Lunardi, Abstract quasilinear parabolic equations, Math. Annalen, 267 (1984), 395-415.
doi: 10.1007/BF01456097. |
[6] |
A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhäuser Verlag, Basel, 1995.
doi: 10.1007/978-3-0348-9234-6. |
[7] |
H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ., 18 (1978), 221-227. |
[8] |
H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Tokyo, 30 (1984), 645-673. |
[9] |
H. Matano, Strongly order-preserving local semi-dynamical systems - theory and applications, in "Semigroups, Theory and Applications" I, Pitman Res. Notes Math. Ser., 141, Longman Sci. Tech., Harlow, (1986). |
[10] |
H. Matano, Asymptotic behavior of solutions of semilinear heat equations on $S^1$, in "Nonlinear Diffusion Equations and Their Equilibrium States" II ( eds. W.-M. Ni, L. A. Peletier and J. Serrin), Math. Sci. Res. Inst. Publ., 13, Springer, (1988), 139-162.
doi: 10.1007/978-1-4613-9608-6_8. |
[11] |
H. Matano, K. -I. Nakamura and B. Lou, Periodic traveling waves in a two-dimensional cylinder with saw-toothed boundary and their homogenization limit, Netw. Heterog. Media, 1 (2006), 537-568.
doi: 10.3934/nhm.2006.1.537. |
[12] |
G. Namah and J.-M. Roquejoffre, Convergence to periodic fronts in a class of semilinear parabolic equations, NoDEA Nonlinear Differential Equations Appl., 4 (1997), 521-536.
doi: 10.1007/s000300050029. |
[13] |
T. Ogiwara and H. Matano, Monotonicity and convergence results in order-preserving systems in the presence of symmetry, Discrete Contin. Dynam. Systems, 5 (1999), 1-34. |
[14] |
T. Ogiwara and K.-I. Nakamura, Spiral traveling wave solutions of nonlinear diffusion equation related to a model of spiral crystal growth, Publ. Res. Inst. Math. Sci., 39 (2003), 767-783. |
[15] |
P. Poláčik, Convergence in smooth strongly monotone flows defined by semilinear parabolic equations, J. Differential Equations, 79 (1989), 89-110.
doi: 10.1016/0022-0396(89)90115-0. |
[16] |
H. L. Smith and H. R. Thieme, Quasi convergence and stability for strongly order-preserving semiflows, SIAM J. Math. Anal., 21 (1990), 673-692.
doi: 10.1137/0521036. |
[17] |
H. L. Smith and H. R. Thieme, Convergence for strongly order-preserving semiflows, SIAM J. Math. Anal., 22 (1991), 1081-1101.
doi: 10.1137/0522070. |
[18] |
T. I. Zelenyak, Stabilisation of solution of boundary value problems for a second-order equation with one space variable, Differ. Equations, 4 (1968), 17-22. |
[1] |
M. W. Hirsch, Hal L. Smith. Asymptotically stable equilibria for monotone semiflows. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 385-398. doi: 10.3934/dcds.2006.14.385 |
[2] |
Yurii Nesterov, Laura Scrimali. Solving strongly monotone variational and quasi-variational inequalities. Discrete and Continuous Dynamical Systems, 2011, 31 (4) : 1383-1396. doi: 10.3934/dcds.2011.31.1383 |
[3] |
Juan A. Calzada, Rafael Obaya, Ana M. Sanz. Continuous separation for monotone skew-product semiflows: From theoretical to numerical results. Discrete and Continuous Dynamical Systems - B, 2015, 20 (3) : 915-944. doi: 10.3934/dcdsb.2015.20.915 |
[4] |
Monica Lazzo, Paul G. Schmidt. Monotone local semiflows with saddle-point dynamics and applications to semilinear diffusion equations. Conference Publications, 2005, 2005 (Special) : 566-575. doi: 10.3934/proc.2005.2005.566 |
[5] |
Marco Spadini. Branches of harmonic solutions to periodically perturbed coupled differential equations on manifolds. Discrete and Continuous Dynamical Systems, 2006, 15 (3) : 951-964. doi: 10.3934/dcds.2006.15.951 |
[6] |
Li Ma, Chong Li, Lin Zhao. Monotone solutions to a class of elliptic and diffusion equations. Communications on Pure and Applied Analysis, 2007, 6 (1) : 237-246. doi: 10.3934/cpaa.2007.6.237 |
[7] |
Michele Campiti, Giovanni P. Galdi, Matthias Hieber. Global existence of strong solutions for $2$-dimensional Navier-Stokes equations on exterior domains with growing data at infinity. Communications on Pure and Applied Analysis, 2014, 13 (4) : 1613-1627. doi: 10.3934/cpaa.2014.13.1613 |
[8] |
Hiroshi Watanabe. Existence and uniqueness of entropy solutions to strongly degenerate parabolic equations with discontinuous coefficients. Conference Publications, 2013, 2013 (special) : 781-790. doi: 10.3934/proc.2013.2013.781 |
[9] |
Dung Le. Partial regularity of solutions to a class of strongly coupled degenerate parabolic systems. Conference Publications, 2005, 2005 (Special) : 576-586. doi: 10.3934/proc.2005.2005.576 |
[10] |
Fuqin Sun, Mingxin Wang. Non-existence of global solutions for nonlinear strongly damped hyperbolic systems. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 949-958. doi: 10.3934/dcds.2005.12.949 |
[11] |
Keonhee Lee, Arnoldo Rojas. Eventually expansive semiflows. Communications on Pure and Applied Analysis, , () : -. doi: 10.3934/cpaa.2022102 |
[12] |
Andrzej Świȩch. Pointwise properties of $ L^p $-viscosity solutions of uniformly elliptic equations with quadratically growing gradient terms. Discrete and Continuous Dynamical Systems, 2020, 40 (5) : 2945-2962. doi: 10.3934/dcds.2020156 |
[13] |
Wei Feng, Weihua Ruan, Xin Lu. On existence of wavefront solutions in mixed monotone reaction-diffusion systems. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 815-836. doi: 10.3934/dcdsb.2016.21.815 |
[14] |
Sergiu Aizicovici, Simeon Reich. Anti-periodic solutions to a class of non-monotone evolution equations. Discrete and Continuous Dynamical Systems, 1999, 5 (1) : 35-42. doi: 10.3934/dcds.1999.5.35 |
[15] |
Rui Li, Yuan Lou. Some monotone properties for solutions to a reaction-diffusion model. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 4445-4455. doi: 10.3934/dcdsb.2019126 |
[16] |
Sabri Bensid, Jesús Ildefonso Díaz. On the exact number of monotone solutions of a simplified Budyko climate model and their different stability. Discrete and Continuous Dynamical Systems - B, 2019, 24 (3) : 1033-1047. doi: 10.3934/dcdsb.2019005 |
[17] |
Alfonso Castro, Benjamin Preskill. Existence of solutions for a semilinear wave equation with non-monotone nonlinearity. Discrete and Continuous Dynamical Systems, 2010, 28 (2) : 649-658. doi: 10.3934/dcds.2010.28.649 |
[18] |
Xin Xu. Existence of monotone positive solutions of a neighbour based chemotaxis model and aggregation phenomenon. Communications on Pure and Applied Analysis, 2020, 19 (9) : 4327-4348. doi: 10.3934/cpaa.2020195 |
[19] |
Mengyu Cheng, Zhenxin Liu. Periodic, almost periodic and almost automorphic solutions for SPDEs with monotone coefficients. Discrete and Continuous Dynamical Systems - B, 2021, 26 (12) : 6425-6462. doi: 10.3934/dcdsb.2021026 |
[20] |
Jon Aaronson, Dalia Terhesiu. Local limit theorems for suspended semiflows. Discrete and Continuous Dynamical Systems, 2020, 40 (12) : 6575-6609. doi: 10.3934/dcds.2020294 |
2021 Impact Factor: 1.41
Tools
Metrics
Other articles
by authors
[Back to Top]