Stochastic Traveling Wave Solution to a Stochastic KPP EquationSpringer Science and Business Media LLC - Tập 28 - Trang 389-417 - 2015
Zhehao Huang, Zhengrong Liu, Zhenzhen Wang
In this paper, we consider the stochastic KPP equation which is perturbed by an environmental noise. Applying an extended stochastic ordering technique, we establish the existence of a stochastic traveling wave solution to the equation and give a sufficient condition under which solutions can be attracted to the stochastic traveling wave.
Spatial Propagation for an Epidemic Model in a Patchy EnvironmentSpringer Science and Business Media LLC - - Trang 1-25 - 2023
Zhaoquan Xu, Tianwei Tan, Cheng-Hsiung Hsu
This paper investigates the propagation dynamics for an epidemic model with nonlinear incidence rates in a patchy environment. Giving a general setting of the nonlinear incidence rates (monotone or non-monotone), we establish a framework that provides a complete characterization on the existence, non-existence and minimal wave speed of traveling waves which describe the evolution of disease starti...... hiện toàn bộ
Heteroclinic orbits in singular systems: A unifying approachSpringer Science and Business Media LLC - Tập 6 - Trang 147-173 - 1994
Flaviano Battelli
We consider singularly perturbed systems
$$\xi = f(\xi ,\eta ,\varepsilon ),\dot \eta = \varepsilon g(\xi ,\eta ,\varepsilon )$$
, such thatξ=f(ξ, αo, 0). αo∃ℝ
m
, has a heteroclinic orbitu(t). We construct a bifurcation functionG(α, ɛ) such that the singular system ha...... hiện toàn bộ
Regular Polygonal Equilibria on $$\mathbb {S}^1$$ and Stability of the Associated Relative EquilibriaSpringer Science and Business Media LLC - Tập 33 - Trang 1071-1086 - 2020
Xiang Yu, Shuqiang Zhu
For the curved n-body problem in
$$\mathbb {S}^3$$
, we show that a regular polygonal configuration for n masses on a geodesic is an equilibrium if and only if n is odd and the masses are equal. The equilibrium is associated with a one-parameter family (depending on the angular velocity) of relativ...... hiện toàn bộ
Renormalization Group Method. Applications to Partial Differential EquationsSpringer Science and Business Media LLC - Tập 13 - Trang 275-321 - 2001
I. Moise, M. Ziane
Our aim in this article is to present a simplified form of the renormalization group (RG) method introduced by Chen, Goldenfeld, and Oono and to derive a rigorous study of the validity in time of the asymptotic solutions furnished by the RG method. We apply the renormalization group method to a slightly compressible fluid equation and to the Swift–Hohenberg equation.
Propagation Dynamics for Time–Space Periodic and Partially Degenerate Reaction–Diffusion Systems with Time DelaySpringer Science and Business Media LLC - - Trang 1-33
Huang, Mingdi, Wu, Shi-Liang, Zhao, Xiao-Qiang
This paper is concerned with the propagation dynamics of a large class of time–space periodic and partially degenerate reaction–diffusion systems with time delay and monostable nonlinearity. In the cooperative case, based on the theory of principal eigenvalues for linear and partially degenerate systems with time delay, we establish the existence of spreading speeds and its coincidence with the mi...... hiện toàn bộ
On a Differential Equation with State-Dependent DelaySpringer Science and Business Media LLC - Tập 24 - Trang 197-248 - 2012
Eugen Stumpf
We study a family of scalar differential equations with a single parameter a > 0 and delay r > 0. In the case of the constant delay r = 1 it is known that for parameters 0 < a < 1 the trivial solution of this family is asymptotically stable, whereas for a > 1 the trivial solution gets unstable, and a global center-unstable manifold connects the trivial solution to a slowly oscillating periodic orb...... hiện toàn bộ
Existence of a Global Attractor for the Heat Equation with Degenerate MemorySpringer Science and Business Media LLC - Tập 35 - Trang 845-864 - 2021
J. C. O. Faria, C. M. Webler
We analyze the long-time behavior of the semigroup S(t) generated by a heat equation with degenerate past history and a nonlinear heat supply posed in a three dimensional bounded domain
$$\Omega $$
. Assuming that the degeneracy occurs in a positive measure subset of
...... hiện toàn bộ