Results 31 to 40 of about 439 (72)
Notes on a PDE System for Biological Network Formation [PDF]
, 2015 We present new analytical and numerical results for the elliptic-parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks.
Haskovec, Jan +3 more
core +4 more sources
Bifurcations from the orbit of solutions of the Neumann problem
, 2017 The purpose of this paper is to study weak solutions of a nonlinear Neumann problem considered on a ball. Assuming that the potential is invariant, we consider an orbit of critical points, i.e. we do not assume that critical points are isolated. We apply
Gołębiewska, Anna +2 more
core +1 more source
Demonstratio MathematicaThis article is concerned with the following Kirchhoff equation: −a+b∫R3∣∇u∣2dxΔu=g(u)+h(x)inR3,-\left(a+b\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=g\left(u)+h\left(x)\hspace{1em}{\rm{in}}\hspace{0.33em ...
Huang Lanxin, Su Jiabao
doaj +1 more source
Dynamics in a predator-prey model with predation-driven Allee effect and memory effect
Open MathematicsIn this article, a diffusive predator-prey model with memory effect and predation-driven Allee effect is considered. Through eigenvalue analysis, the local asymptotic stability of positive constant steady-state solutions is analyzed, and it is found that
Zhang Huiwen, Jin Dan
doaj +1 more source
European Journal of Applied MathematicsThis paper studies the spatio-temporal dynamics of a diffusive plant-sulphide model with toxicity delay. More specifically, the effects of discrete delay and distributed delay on the dynamics are explored, respectively.
Yonghui Xia, Jianglong Xiao, Jianshe Yu
doaj +1 more source
Defect Modes and Homogenization of Periodic Schr\"odinger Operators
, 2011 We consider the discrete eigenvalues of the operator $H_\eps=-\Delta+V(\x)+\eps^2Q(\eps\x)$, where $V(\x)$ is periodic and $Q(\y)$ is localized on $\R^d,\ \ d\ge1$.
Bechouche P. +2 more
core +1 more source
Slow passage through the Busse balloon – predicting steps on the Eckhaus staircase
European Journal of Applied MathematicsMotivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealised Ginzburg–Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting target states ...
Anna Asch +3 more
doaj +1 more source
Advances in Nonlinear AnalysisWe study stationary solutions of McKean–Vlasov equation on a high-dimensional sphere and other compact Riemannian manifolds. We extend the equivalence of the energetic problem formulation to the manifold setting and characterize critical points of the ...
Shalova Anna, Schlichting André
doaj +1 more source
Effects of anisotropic diffusion in a two-dimensional unstirred chemostat
Advanced Nonlinear StudiesWe investigate an unstirred chemostat model in which two species compete in a two-dimensional environment. The populations are assumed to disperse anisotropically, with distinct probabilities assigned to horizontal and vertical movements, which are ...
Yu Hongqiang, Wu Jianhua
doaj +1 more source
European Journal of Applied MathematicsWe study the Cauchy problem on the real line for the nonlocal Fisher-KPP equation in one spatial dimension, \begin{equation*} u_t = D u_{xx} + u(1-\phi *u), \end{equation*} where $\phi *u$ is a spatial convolution with the top hat kernel,
David John Needham +3 more
doaj +1 more source