Fiedler, Bernold; Rocha, Carlos Boundary orders and geometry of the signed Thom-Smale complex for Sturm global attractors. (English) Zbl 1503.35040 J. Dyn. Differ. Equations 34, No. 4, 2787-2818 (2022). MSC: 35B41 35K20 35K58 37D15 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Dyn. Differ. Equations 34, No. 4, 2787--2818 (2022; Zbl 1503.35040) Full Text: DOI arXiv OpenURL
Moreira, Estefani M.; Valero, José Structure of the attractor for a non-local Chafee-Infante problem. (English) Zbl 1479.35132 J. Math. Anal. Appl. 507, No. 2, Article ID 125801, 25 p. (2022). MSC: 35B41 35K20 35K59 35R09 PDF BibTeX XML Cite \textit{E. M. Moreira} and \textit{J. Valero}, J. Math. Anal. Appl. 507, No. 2, Article ID 125801, 25 p. (2022; Zbl 1479.35132) Full Text: DOI arXiv OpenURL
Valero, José Characterization of the attractor for nonautonomous reaction-diffusion equations with discontinuous nonlinearity. (English) Zbl 1462.35084 J. Differ. Equations 275, 270-308 (2021). MSC: 35B40 35B41 35B51 35K20 35K55 35K57 35R70 PDF BibTeX XML Cite \textit{J. Valero}, J. Differ. Equations 275, 270--308 (2021; Zbl 1462.35084) Full Text: DOI OpenURL
Fiedler, Bernold; Rocha, Carlos Sturm 3-ball global attractors 2: design of Thom-Smale complexes. (English) Zbl 1423.35040 J. Dyn. Differ. Equations 31, No. 3, 1549-1590 (2019). MSC: 35B41 37D15 05C90 57N60 35K58 37B30 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Dyn. Differ. Equations 31, No. 3, 1549--1590 (2019; Zbl 1423.35040) Full Text: DOI arXiv OpenURL
Fiedler, Bernold; Rocha, Carlos Sturm 3-ball global attractors 3: examples of Thom-Smale complexes. (English) Zbl 1396.37036 Discrete Contin. Dyn. Syst. 38, No. 7, 3479-3545 (2018). MSC: 37D15 35B41 05C90 57N60 35K59 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, Discrete Contin. Dyn. Syst. 38, No. 7, 3479--3545 (2018; Zbl 1396.37036) Full Text: DOI arXiv OpenURL
Fiedler, Bernold; Rocha, Carlos Sturm 3-ball global attractors. 1: Thom-Smale complexes and meanders. (English) Zbl 1408.37027 São Paulo J. Math. Sci. 12, No. 1, 18-67 (2018). MSC: 37B30 35B41 35K59 35K20 37C70 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, São Paulo J. Math. Sci. 12, No. 1, 18--67 (2018; Zbl 1408.37027) Full Text: DOI arXiv OpenURL
Pimentel, Edgard A.; Pimentel, Juliana F. S. Estimates for a class of slowly non-dissipative reaction-diffusion equations. (English) Zbl 1358.35057 Rocky Mt. J. Math. 46, No. 3, 1011-1028 (2016). Reviewer: Dian K. Palagachev (Bari) MSC: 35K57 35B65 58J35 PDF BibTeX XML Cite \textit{E. A. Pimentel} and \textit{J. F. S. Pimentel}, Rocky Mt. J. Math. 46, No. 3, 1011--1028 (2016; Zbl 1358.35057) Full Text: DOI Euclid OpenURL
Fiedler, Bernold; Rocha, Carlos Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems. (English) Zbl 1375.35259 J. Dyn. Differ. Equations 27, No. 3-4, 597-626 (2015). MSC: 35K59 35A24 35K20 35K57 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Dyn. Differ. Equations 27, No. 3--4, 597--626 (2015; Zbl 1375.35259) Full Text: DOI OpenURL
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José Regular solutions and global attractors for reaction-diffusion systems without uniqueness. (English) Zbl 1304.35119 Commun. Pure Appl. Anal. 13, No. 5, 1891-1906 (2014). MSC: 35B41 35B40 35K55 37B25 58C06 35K57 PDF BibTeX XML Cite \textit{O. V. Kapustyan} et al., Commun. Pure Appl. Anal. 13, No. 5, 1891--1906 (2014; Zbl 1304.35119) Full Text: DOI OpenURL
Fiedler, Bernold; Rocha, Carlos Nonlinear Sturm global attractors: unstable manifold decompositions as regular CW-complexes. (English) Zbl 1327.35194 Discrete Contin. Dyn. Syst. 34, No. 12, 5099-5122 (2014). Reviewer: Rodica Luca (Iaşi) MSC: 35K58 35B41 05C90 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, Discrete Contin. Dyn. Syst. 34, No. 12, 5099--5122 (2014; Zbl 1327.35194) Full Text: DOI OpenURL
Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José Structure and regularity of the global attractor of a reaction-diffusion equation with non-smooth nonlinear term. (English) Zbl 1304.35118 Discrete Contin. Dyn. Syst. 34, No. 10, 4155-4182 (2014). MSC: 35B41 35B40 35K55 37L25 58C06 35K57 PDF BibTeX XML Cite \textit{O. V. Kapustyan} et al., Discrete Contin. Dyn. Syst. 34, No. 10, 4155--4182 (2014; Zbl 1304.35118) Full Text: DOI arXiv OpenURL
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias A permutation characterization of Sturm global attractors of Hamiltonian type. (English) Zbl 1233.35042 J. Differ. Equations 252, No. 1, 588-623 (2012). Reviewer: Guy Katriel (Haifa) MSC: 35B41 37L30 37C70 35K20 35K58 PDF BibTeX XML Cite \textit{B. Fiedler} et al., J. Differ. Equations 252, No. 1, 588--623 (2012; Zbl 1233.35042) Full Text: DOI OpenURL
Fila, Marek; Yanagida, Eiji Homoclinic and heteroclinic orbits for a semilinear parabolic equation. (English) Zbl 1252.35157 Tohoku Math. J. (2) 63, No. 4, Centen. Iss., 561-579 (2011). Reviewer: Jens Rademacher (Amsterdam) MSC: 35K58 35K55 35B40 35B41 37C29 35B33 35B51 PDF BibTeX XML Cite \textit{M. Fila} and \textit{E. Yanagida}, Tôhoku Math. J. (2) 63, No. 4, 561--579 (2011; Zbl 1252.35157) Full Text: DOI OpenURL
Fiedler, Bernold; Rocha, Carlos Connectivity and design of planar global attractors of Sturm type. III: Small and platonic examples. (English) Zbl 1204.35106 J. Dyn. Differ. Equations 22, No. 2, 121-162 (2010). MSC: 35K58 35B41 35K20 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Dyn. Differ. Equations 22, No. 2, 121--162 (2010; Zbl 1204.35106) Full Text: DOI OpenURL
Ghrist, R. W.; Vandervorst, R. C. Scalar parabolic PDEs and braids. (English) Zbl 1172.35039 Trans. Am. Math. Soc. 361, No. 5, 2755-2788 (2009). Reviewer: Cristian Chifu (Cluj-Napoca) MSC: 35K90 37B30 PDF BibTeX XML Cite \textit{R. W. Ghrist} and \textit{R. C. Vandervorst}, Trans. Am. Math. Soc. 361, No. 5, 2755--2788 (2009; Zbl 1172.35039) Full Text: DOI arXiv OpenURL
Fiedler, Bernold; Rocha, Carlos Connectivity and design of planar global attractors of Sturm type. II: Connection graphs. (English) Zbl 1179.35069 J. Differ. Equations 244, No. 5, 1255-1286 (2008). MSC: 35B41 35K58 35K20 37L30 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Differ. Equations 244, No. 5, 1255--1286 (2008; Zbl 1179.35069) Full Text: DOI OpenURL
Rocha, Carlos Realization of period maps of planar Hamiltonian systems. (English) Zbl 1149.34004 J. Dyn. Differ. Equations 19, No. 3, 571-591 (2007). Reviewer: Maite Grau (Lleida) MSC: 34A55 35B41 37G35 34C25 PDF BibTeX XML Cite \textit{C. Rocha}, J. Dyn. Differ. Equations 19, No. 3, 571--591 (2007; Zbl 1149.34004) Full Text: DOI OpenURL
Fiedler, Bernold; Rocha, Carlos; Wolfrum, Matthias Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle. (English) Zbl 1064.35076 J. Differ. Equations 201, No. 1, 99-138 (2004). Reviewer: Arnd Scheel (Minneapolis) MSC: 35K55 37L30 37C29 35B05 PDF BibTeX XML Cite \textit{B. Fiedler} et al., J. Differ. Equations 201, No. 1, 99--138 (2004; Zbl 1064.35076) Full Text: DOI OpenURL
Wolfrum, Matthias A sequence of order relations: Encoding heteroclinic connections in scalar parabolic PDE. (English) Zbl 1004.35025 J. Differ. Equations 183, No. 1, 56-78 (2002). Reviewer: Dian K.Palagachev (Bari) MSC: 35B41 35K55 35B05 PDF BibTeX XML Cite \textit{M. Wolfrum}, J. Differ. Equations 183, No. 1, 56--78 (2002; Zbl 1004.35025) Full Text: DOI OpenURL
Fiedler, Bernold; Rocha, Carlos Realization of meander permutations by boundary value problems. (English) Zbl 0935.34018 J. Differ. Equations 156, No. 2, 282-308 (1999). Reviewer: J.Andres (Olomouc) MSC: 34B15 37D15 37C15 37B25 34C60 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{C. Rocha}, J. Differ. Equations 156, No. 2, 282--308 (1999; Zbl 0935.34018) Full Text: DOI Link OpenURL
Härterich, Jörg Attractors of viscous balance laws: Uniform estimates for the dimension. (English) Zbl 0897.35041 J. Differ. Equations 142, No. 1, 188-211 (1998). Reviewer: B.Scarpellini (Basel) MSC: 35K60 35B25 35B40 PDF BibTeX XML Cite \textit{J. Härterich}, J. Differ. Equations 142, No. 1, 188--211 (1998; Zbl 0897.35041) Full Text: DOI Link OpenURL
Kokubu, Hiroshi; Mischaikow, Konstantin; Nishiura, Yasumasa; Oka, Hireo; Takaishi, Takeshi Connecting orbit structure of monotone solutions in the shadow system. (English) Zbl 0902.35058 J. Differ. Equations 140, No. 2, 309-364 (1997). Reviewer: S.Jimbo (Sapporo) MSC: 35K60 37C70 PDF BibTeX XML Cite \textit{H. Kokubu} et al., J. Differ. Equations 140, No. 2, 309--364 (1997; Zbl 0902.35058) Full Text: DOI Link OpenURL
Fusco, G.; Verduyn Lunel, Sjoerd M. Order structures and the heat equation. (English) Zbl 0897.35036 J. Differ. Equations 139, No. 1, 104-145 (1997). Reviewer: P.Polacik (Bratislava) MSC: 35K20 35B05 35B50 PDF BibTeX XML Cite \textit{G. Fusco} and \textit{S. M. Verduyn Lunel}, J. Differ. Equations 139, No. 1, 104--145 (1997; Zbl 0897.35036) Full Text: DOI OpenURL
Friesecke, G.; McLeod, J. B. Dynamics as a mechanism preventing the formation of finer and fine microstructure. (English) Zbl 0920.73345 Arch. Ration. Mech. Anal. 133, No. 3, 199-247 (1996). MSC: 74A60 74M25 35Q72 PDF BibTeX XML Cite \textit{G. Friesecke} and \textit{J. B. McLeod}, Arch. Ration. Mech. Anal. 133, No. 3, 199--247 (1996; Zbl 0920.73345) Full Text: DOI OpenURL
Vishnevskij, M. P.; Zelenyak, T. I.; Lavrent’ev, M. M. jun. Behavior of solutions to nonlinear parabolic equations at large time. (English. Russian original) Zbl 0863.35051 Sib. Math. J. 36, No. 3, 435-453 (1995); translation from Sib. Mat. Zh. 36, No. 3, 510-530 (1995). Reviewer: P.Polacik (Bratislava) MSC: 35K60 35B40 35B05 35B35 PDF BibTeX XML Cite \textit{M. P. Vishnevskij} et al., Sib. Math. J. 36, No. 3, 435--453 (1995; Zbl 0863.35051); translation from Sib. Mat. Zh. 36, No. 3, 510--530 (1995) Full Text: DOI OpenURL
Babin, Anatoli V. Symmetrization properties of parabolic equations in symmetric domains. (English) Zbl 0807.35065 J. Dyn. Differ. Equations 6, No. 4, 639-658 (1994). MSC: 35K60 35B40 58J70 35K35 PDF BibTeX XML Cite \textit{A. V. Babin}, J. Dyn. Differ. Equations 6, No. 4, 639--658 (1994; Zbl 0807.35065) Full Text: DOI OpenURL
Freitas, Pedro Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations. (English) Zbl 0807.35068 J. Dyn. Differ. Equations 6, No. 4, 613-629 (1994). MSC: 35K60 35K57 34B15 35B32 35B35 PDF BibTeX XML Cite \textit{P. Freitas}, J. Dyn. Differ. Equations 6, No. 4, 613--629 (1994; Zbl 0807.35068) Full Text: DOI OpenURL
Fiedler, Bernold; Mischaikow, Konstantin Dynamics of bifurcations for variational problems with \(O(3)\) equivariance: A Conley index approach. (English) Zbl 0756.49003 Arch. Ration. Mech. Anal. 119, No. 2, 145-196 (1992). Reviewer: B.Fiedler MSC: 49J20 58E07 35K57 58E05 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{K. Mischaikow}, Arch. Ration. Mech. Anal. 119, No. 2, 145--196 (1992; Zbl 0756.49003) Full Text: DOI OpenURL
Poláčik, Peter Complicated dynamics in scalar semilinear parabolic equations in higher space dimension. (English) Zbl 0738.35027 J. Differ. Equations 89, No. 2, 244-271 (1991). Reviewer: A.D.Osborne (Keele) MSC: 35K55 58J35 35K20 PDF BibTeX XML Cite \textit{P. Poláčik}, J. Differ. Equations 89, No. 2, 244--271 (1991; Zbl 0738.35027) Full Text: DOI OpenURL
Alikakos, Nicholas; Bates, Peter W.; Fusco, Giorgio Slow motion for the Cahn-Hilliard equation in one space dimension. (English) Zbl 0753.35042 J. Differ. Equations 90, No. 1, 81-135 (1991). Reviewer: K.Kajitani (Ibaraki) MSC: 35K60 35B40 58J70 37C10 PDF BibTeX XML Cite \textit{N. Alikakos} et al., J. Differ. Equations 90, No. 1, 81--135 (1991; Zbl 0753.35042) Full Text: DOI OpenURL
Fusco, Giorgio; Rocha, Carlos A permutation related to the dynamics of a scalar parabolic PDE. (English) Zbl 0768.35048 J. Differ. Equations 91, No. 1, 111-137 (1991). Reviewer: G.M.Lieberman (Ames) MSC: 35K60 37C10 PDF BibTeX XML Cite \textit{G. Fusco} and \textit{C. Rocha}, J. Differ. Equations 91, No. 1, 111--137 (1991; Zbl 0768.35048) Full Text: DOI OpenURL
Brunovský, Pavol The attractor of the scalar reaction diffusion equation is a smooth graph. (English) Zbl 0726.35021 J. Dyn. Differ. Equations 2, No. 3, 293-323 (1990). Reviewer: M.Fila (Bratislava) MSC: 35B40 35K57 PDF BibTeX XML Cite \textit{P. Brunovský}, J. Dyn. Differ. Equations 2, No. 3, 293--323 (1990; Zbl 0726.35021) Full Text: DOI OpenURL
Brunovský, Pavol The attractor of the scalar reaction diffusion equation is a smooth graph. (English) Zbl 0711.35015 J. Dyn. Differ. Equations 2, No. 3, 293-323 (1990). Reviewer: P.Brunovský MSC: 35B40 35K57 35K55 PDF BibTeX XML Cite \textit{P. Brunovský}, J. Dyn. Differ. Equations 2, No. 3, 293--323 (1990; Zbl 0711.35015) Full Text: DOI OpenURL
Bates, Peter W.; Fife, Paul C. Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and time scales for coarsening. (English) Zbl 0706.58074 Physica D 43, No. 2-3, 335-348 (1990). Reviewer: M.Puta MSC: 58J50 PDF BibTeX XML Cite \textit{P. W. Bates} and \textit{P. C. Fife}, Physica D 43, No. 2--3, 335--348 (1990; Zbl 0706.58074) Full Text: DOI OpenURL
Chow, Shui-Nee; Deng, Bo; Fiedler, Bernold Homoclinic bifurcation at resonant eigenvalues. (English) Zbl 0703.34050 J. Dyn. Differ. Equations 2, No. 2, 177-244 (1990). Reviewer: D.Bobrowski MSC: 34C15 37G99 PDF BibTeX XML Cite \textit{S.-N. Chow} et al., J. Dyn. Differ. Equations 2, No. 2, 177--244 (1990; Zbl 0703.34050) Full Text: DOI OpenURL
Fiedler, Bernold; Mallet-Paret, John A Poincaré-Bendixson theorem for scalar reaction diffusion equations. (English) Zbl 0704.35070 Arch. Ration. Mech. Anal. 107, No. 4, 325-345 (1989). Reviewer: B.D.Sleeman MSC: 35K57 35B99 PDF BibTeX XML Cite \textit{B. Fiedler} and \textit{J. Mallet-Paret}, Arch. Ration. Mech. Anal. 107, No. 4, 325--345 (1989; Zbl 0704.35070) Full Text: DOI OpenURL
Brunovský, P.; Fiedler, B. Connecting orbits in scalar reaction diffusion equations. II: The complete solution. (English) Zbl 0699.35144 J. Differ. Equations 81, No. 1, 106-135 (1989). Reviewer: J.Mawhin MSC: 35K57 PDF BibTeX XML Cite \textit{P. Brunovský} and \textit{B. Fiedler}, J. Differ. Equations 81, No. 1, 106--135 (1989; Zbl 0699.35144) Full Text: DOI OpenURL
Fiedler, Bernold Discrete Lyapunov functionals and \(\omega\)-limit sets. (English) Zbl 0688.58041 RAIRO, Modélisation Math. Anal. Numér. 23, No. 3, 415-431 (1989). Reviewer: G.Warnecke MSC: 58J47 35K60 37C70 35B40 PDF BibTeX XML Cite \textit{B. Fiedler}, RAIRO, Modélisation Math. Anal. Numér. 23, No. 3, 415--431 (1989; Zbl 0688.58041) Full Text: DOI EuDML OpenURL
Angenent, S. B.; Fiedler, B. The dynamics of rotating waves in scalar reaction diffusion equations. (English) Zbl 0696.35086 Trans. Am. Math. Soc. 307, No. 2, 545-568 (1988). MSC: 35K57 37C70 PDF BibTeX XML Cite \textit{S. B. Angenent} and \textit{B. Fiedler}, Trans. Am. Math. Soc. 307, No. 2, 545--568 (1988; Zbl 0696.35086) Full Text: DOI OpenURL