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Existence of 3D Strong Solutions for a System Modeling a Deformable Solid Inside a Viscous Incompressible Fluid
Springer Science and Business Media LLC - Tập 29 - Trang 737-782 - 2015
We study a coupled system modeling the movement of a deformable solid inside a
viscous incompressible fluid. For the solid we consider a given deformation
which has to obey several physical constraints. The motion of the fluid is
modeled by the incompressible Navier–Stokes equations in a time-dependent
bounded domain of $$\mathbb {R}^3$$ , and the solid satisfies the Newton’s laws.
Our contributio...
Stochastic Traveling Wave Solution to a Stochastic KPP Equation
Springer Science and Business Media LLC - Tập 28 - Trang 389-417 - 2015
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 Environment
Springer Science and Business Media LLC - - Trang 1-25 - 2023
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...
Heteroclinic orbits in singular systems: A unifying approach
Springer Science and Business Media LLC - Tập 6 - Trang 147-173 - 1994
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 has a heteroclinic orbit if and only ifG(α, ɛ)=0 has a
solutionα=α(ɛ). We also apply this result to recover some theorems that have
b...
Regular Polygonal Equilibria on $$\mathbb {S}^1$$ and Stability of the Associated Relative Equilibria
Springer Science and Business Media LLC - Tập 33 - Trang 1071-1086 - 2020
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 relative equilibria,
which take place on $$\mathbb {S}^1$$ embedded in $$\mathbb {S}^2$$ . We then
study the...
Renormalization Group Method. Applications to Partial Differential Equations
Springer Science and Business Media LLC - Tập 13 - Trang 275-321 - 2001
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 Delay
Springer Science and Business Media LLC - - Trang 1-33
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...
On the Ambrosio–Figalli–Trevisan Superposition Principle for Probability Solutions to Fokker–Planck–Kolmogorov Equations
Springer Science and Business Media LLC - - 2021
On a Differential Equation with State-Dependent Delay
Springer Science and Business Media LLC - Tập 24 - Trang 197-248 - 2012
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...
Existence of a Global Attractor for the Heat Equation with Degenerate Memory
Springer Science and Business Media LLC - Tập 35 - Trang 845-864 - 2021
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 $$\Omega $$ , we prove the existence and
regularity of the global attractor associated to this semigroup....
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