A new concept of instability and spatial patterns

• Published in: Nonlinear analysis: real world applications Vol. 87; p. 104445
• Main Authors: Kučera, Milan, Klika, Václav, Fencl, Martin, Eisner, Jan
• Format: Journal Article
• Language: English
• 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

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...