This paper deals with a micro–macro derivation of a variety of cross-diffusion models for a
large system of active particles. Some of the models at the macroscopic scale can be viewed …

This paper deals with a parabolic–parabolic Keller–Segel‐type system in a bounded
domain of,{N= 2; 3}, under different boundary conditions, with time‐dependent coefficients …

This paper estimates the blow-up time for the heat equation ut= Δ u with a local nonlinear
Neumann boundary condition: The normal derivative∂ u/∂ n= uq on Γ 1, one piece of the …

In this paper, we obtain upper bounds for the critical time $ T^* $ of the blow-up for the
parabolic-elliptic Patlak-Keller-Segel system on the 2D-Euclidean space. No moment …

This paper deals with a lower bound for the blow-up time for solutions of the fully parabolic
chemotaxis system {ut=∇⋅[(u+ α) m 1− 1∇ u− χ u (u+ α) m 2− 2∇ v] in Ω×(0, T), vt= Δ v− v+ …

We study the lower bound of the lifespan T^* T∗ for the heat equation u_t= Δ u ut= Δ u in a
bounded domain Ω ⊂ R^ n (n ≥ 2) Ω⊂ R n (n≥ 2) with positive initial data u_ 0 u 0 and a …

In a recent study, a lower bound is established on the blow up time for solutions of a
chemotaxis system, with nonlinear chemotactic sensitivity u (u+ 1) m− 1, set in the three …

In this paper, we consider the initial boundary value problem for the three species
cooperating model under various boundary conditions in which the solution may blow up in …

This paper is concerned with a general fully parabolic Keller-Segel system, defined in a
convex bounded and smooth domain Ω of RN, for N∈{2, 3}, with coefficients depending on …

This paper deals with the blow-up of the solution for a system of evolution p-Laplacian
equations uit= div (|∇ ui| p− 2∇ ui)(i= 1, 2,..., k) with nonlinear boundary flux. Under certain …