A new concept of instability and spatial patterns
Non-standard notions of instability and spatial patterns are introduced and their robustness is proved. In fact, these notions correspond to what is really usually done in numerical computations or in a laboratory. Situations are described when our patterns evolve due to the newly introduced instabi...
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| Published in | Nonlinear analysis: real world applications Vol. 87; p. 104445 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
01.02.2026
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| Online Access | Get full text |
| ISSN | 1468-1218 |
| DOI | 10.1016/j.nonrwa.2025.104445 |
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| Abstract | Non-standard notions of instability and spatial patterns are introduced and their robustness is proved. In fact, these notions correspond to what is really usually done in numerical computations or in a laboratory. Situations are described when our patterns evolve due to the newly introduced instability of the basic homogeneous steady state even if it is stable and even if heterogeneous stationary solutions do not exist. |
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| AbstractList | Non-standard notions of instability and spatial patterns are introduced and their robustness is proved. In fact, these notions correspond to what is really usually done in numerical computations or in a laboratory. Situations are described when our patterns evolve due to the newly introduced instability of the basic homogeneous steady state even if it is stable and even if heterogeneous stationary solutions do not exist. |
| ArticleNumber | 104445 |
| Author | Eisner, Jan Klika, Václav Kučera, Milan Fencl, Martin |
| Author_xml | – sequence: 1 givenname: Milan orcidid: 0000-0001-6033-369X surname: Kučera fullname: Kučera, Milan email: kucera@math.cas.cz organization: Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 11567 Prague 1, Czech Republic – sequence: 2 givenname: Václav orcidid: 0000-0001-6272-8396 surname: Klika fullname: Klika, Václav email: vaclav.klika@fjfi.cvut.cz organization: Department of Mathematics, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic – sequence: 3 givenname: Martin orcidid: 0000-0003-3646-0319 surname: Fencl fullname: Fencl, Martin email: fenclm37@kma.zcu.cz organization: Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, 30100 Pilsen, Czech Republic – sequence: 4 givenname: Jan orcidid: 0000-0001-5046-8849 surname: Eisner fullname: Eisner, Jan email: jeisner@prf.jcu.cz organization: Department of Mathematics, Faculty of Science, University of South Bohemia, Branišovská1760, 37005 České Budějovice, Czech Republic |
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| Cites_doi | 10.1103/PhysRevE.96.022212 10.1016/j.anihpc.2010.09.001 10.1016/0362-546X(88)90051-X 10.1103/PhysRevLett.133.047202 10.1111/j.1749-6632.1979.tb29492.x 10.1137/0513037 10.1007/BF00289234 10.1098/rsta.2020.0268 10.1017/S0956792523000141 10.1137/0907024 10.2307/1970100 10.1098/rspa.2022.0829 10.1098/rstb.1952.0012 10.1016/j.physd.2020.132735 10.1007/s004400050074 10.1007/s11538-013-9914-6 10.1016/0022-0396(87)90173-2 |
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| Keywords | Gierer-Meinhardt system Reaction–diffusion systems 35B36 92C15 35B35 Non-standard patterns Almost non-evolving solutions Non-standard instability Spatial patterns 35K57 |
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