Finite Time Collapse in Chemotaxis Systems with Logistic-Type Superlinear Source

Mathematical analysis of a quasilinear Keller-Segel system modeling chemotaxis on a ball domain in n-dimensional space. The research by Monica Marras from the University of Cagliari investigates conditions for finite-time blow-up of solutions. It provides a lower bound for the lifespan or blow-up time, with an explicitly computable bound for three-dimensional cases.

Use Cases

• Simulating finite-time blow-up in chemotaxis models based on the described Keller-Segel system.
• Analyzing the effect of logistic-type superlinear source terms on solution stability.
• Benchmarking numerical solvers for partial differential equations against derived lower bounds for blow-up time.
• Studying the relationship between L^p-norm and L^∞-norm blow-up in parabolic systems.

Strengths

• Analysis is grounded in a specific, well-defined mathematical model (Keller-Segel system).
• Provides explicit, computable lower bounds for blow-up time in three-dimensional cases.
• The source term parameters (λ, μ, k) are clearly defined, allowing for reproducibility.

Limitations

• Description metadata is limited; actual data quality requires manual inspection after download.
• Column-level documentation is absent; field semantics must be inferred after download.
• Row count is unknown, which may limit suitability assessment.

Provenance

Source

University of Cagliari

Collection Method

Theoretical mathematical analysis.

Geography

Analysis is performed on a ball domain in ℝⁿ, n≥3.