Properties of given and detected unbounded solutions to a class of chemotaxis models

• DOI: 10.1111/sapm.12627
• Publication Date: 2023-08-09T11:54:30Z
• Authors: Alessandro Columbu; Silvia Frassu; Giuseppe Viglialoro
• Keywords: Semi-infinite; Blowing up

Abstract This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for rather general attraction–repulsion model, nonlinear productions, diffusion, sensitivities, and logistic term, we detect Lebesgue spaces where given also blow up in the corresponding norms those spaces; subsequently, estimates blow‐up time are established. Finally, simplified version some criteria proved. More precisely, analyze zero‐flux system essentially described as The problem is formulated bounded smooth domain Ω , . A sufficiently regular initial data fixed. Under specific relations involving above parameters, one these always requiring largeness conditions on prove that any solution (), blowing at finite becomes ‐norm, all ; give lower bounds T (depending ) aforementioned being whenever establish sufficient parameters ensuring u 0 () effectively time. Within context phenomena connected this research partially improves analysis Wang et al. ( J Math Anal Appl 2023;518(1):126679) and, moreover, contributes enrich level knowledge topic.