Global existence and boundedness in a quasilinear attraction-repulsion chemotaxis system of parabolic-elliptic type

A priori bounds and global existence for a strongly coupled quasilinear parabolic system modeling chemotaxis

A priori bounds are found for solutions to a strongly coupled reactiondiffusion system that models competition of species in the presence of chemotaxis. These bounds are used to prove the existence of global solutions.

Boundedness in a Three-dimensional Attraction-repulsion Chemotaxis System with Nonlinear Diffusion and Logistic Source

This article concerns the attraction-repulsion chemotaxis system with nonlinear diffusion and logistic source, ut = ∇ · ((u+ 1)m−1∇u)−∇ · (χu∇v) +∇ · (ξu∇w) + ru− μu , x ∈ Ω, t > 0, vt = ∆v + αu− βv, x ∈ Ω, t > 0, wt = ∆w + γu− δw, x ∈ Ω, t > 0 under Neumann boundary conditions in a bounded domain Ω ⊂ R3 with smooth boundary. We show that if the diffusion is strong enough or the logistic dampen...

Global existence of solutions to a parabolic-elliptic chemotaxis system with critical degenerate di ffusion

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Existence of at least three weak solutions for a quasilinear elliptic system

In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...