47 citations · 55 across the 8 of their papers we have counts for
9 papers
Blow-down and immediate onset of positivity in the Neumann problem for (super-)fast diffusion equations
Youshan Tao, Michael Winkler
For the degenerate parabolic equation , the homogeneous Neumann problem in smoothly bounded domains is considered in th…
Preventing blow-up by local anisotropy of signal production in the Keller-Segel system with strongly differing diffusion rates
Youshan Tao, Michael Winkler
In a smoothly bounded domain , , the manuscript considers the variant of the Keller-Segel system given by \[ \left\{ \begin{array}{l} u_t = D Δu - \nabla \cdo…
A switch in dimension dependence of critical blow-up exponents in a Keller-Segel system involving indirect signal production
Youshan Tao, Michael Winkler
In bounded -dimensional domains with , this manuscript considers an initial-boundary problem for a quasilinear chemotaxis system with indirect attractant production, as…
Asymptotic stability of spatial homogeneity in a haptotxis model for oncolytic virotherapy
Youshan Tao, Michael Winkler
This work considers a model for oncolytic virotherapy, as given by the reaction-diffusion-taxis system $$ \left\{ \begin{array}{l} u_t = Δu - \nabla \cdot (u\nabla v)-ρuz, \\[1mm]…
Existence theory and qualitative analysis for a fully cross-diffusive predator-prey system
Youshan Tao, Michael Winkler
This manuscript considers a Neumann initial-boundary value problem for the predator-prey system $$ \left\{ \begin{array}{l} u_t = D_1 u_{xx} - χ_1 (uv_x)_x + u(λ_1-u+a_1 v), \\[1mm…
Analysis of a one-dimensional forager-exploiter model
Youshan Tao, Michael Winkler
\begin{abstract} \noindent % We consider the one-dimensional parabolic system The system \bas \left\{ \begin{array}{l} u_t= u_{xx} - χ_1 (uw_x)_x, \\[1mm] v_t = v_{xx} - χ_2 (vu_x)…
Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production
Youshan Tao, Michael Winkler
We study the Neumann initial-boundary problem for the chemotaxis system $$ \left\{\begin{array}{ll} u_t= Δu - \nabla \cdot (u\nabla v), & x\in Ω, \, t>0, 0=Δv - μ(t)+w, & x\in Ω, \…
Boundedness in a two-dimensional chemotaxis-haptotaxis system
Youshan Tao
This work studies the chemotaxis-haptotaxis system $$\left\{ \begin{array}{ll} u_t= Δu - χ\nabla \cdot (u\nabla v) - ξ\nabla \cdot (u\nabla w) + μu(1-u-w), &\qquad x\in Ω, \, t>0,…
Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity
Youshan Tao, Michael Winkler
We consider the quasilinear parabolic-parabolic Keller-Segel system $$ u_t=\nabla \cdot (D(u)\nabla u) - \nabla \cdot (S(u)\nabla v), \qquad x\inΩ, \ t>0, v_t=Δv -v + u, x\inΩ, \ t…