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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Bibliographic Details
Published inNonlinear analysis: real world applications Vol. 87; p. 104445
Main Authors Kučera, Milan, Klika, Václav, Fencl, Martin, Eisner, Jan
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.02.2026
Subjects
Almost non-evolving solutions
Gierer-Meinhardt system
Non-standard instability
Non-standard patterns
Reaction–diffusion systems
Spatial patterns
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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Summary: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.
ISSN:1468-1218
DOI:10.1016/j.nonrwa.2025.104445