Communications on Pure & Applied Analysis
October 2021 , Volume 20 , Issue 10
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In this paper, we consider a two-group SIR epidemic model with bilinear incidence in a patchy environment. It is assumed that the infectious disease has a fixed latent period and spreads between two groups. Firstly, when the basic reproduction number
We present a generalization of the most usual symmetries in differential equations known as the time-reversibility and the equivariance ones. We check that the typical properties are also valid for the new definition that unifies both. With it, we are able to present new families of planar polynomial vector fields having equilibrium points of center type. Moreover, we provide the highest lower bound for the local cyclicity of an equilibrium point of polynomial vector fields of degree 6,
In this paper, we consider the following Schrödinger equation with singular potential:
Our purpose in this paper is to classify the non-topological solutions of equations
and with total magnetic flux
A parabolic free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at different voltages. The model couples a fourth-order semilinear parabolic equation for the deformation of the top plate to a Laplace equation for the electrostatic potential in the device. The strength of the coupling is tuned by a parameter
We obtain characterizations of nonuniform dichotomies, defined by general growth rates, based on admissibility conditions. Additionally, we use the obtained characterizations to derive robustness results for the considered dichotomies. As particular cases, we recover several results in the literature concerning nonuniform exponential dichotomies and nonuniform polynomial dichotomies as well as new results for nonuniform dichotomies with logarithmic growth.
It is established existence of ground and bound state solutions for Choquard equation considering concave-convex nonlinearities in the following form
We develop highly anisotropic Carleson measure over multi-level ellipsoid covers
We consider an unconditional fully discrete finite element scheme for a nematic liquid crystal flow with different kinematic transport properties. We prove that the scheme converges towards a unique critical point of the elastic energy subject to the finite element subspace, when the number of time steps go to infinity while the time step and mesh size are fixed. A Lojasiewicz type inequality, which is the key for getting the time asymptotic convergence of the whole sequence furnished by the numerical scheme, is also derived.
We study asymptotically autonomous dynamics for non-autonom-ous stochastic 3D Brinkman-Forchheimer equations with general delays (containing variable delay and distributed delay). We first prove the existence of a pullback random attractor not only in the initial space but also in the regular space. We then prove that, under the topology of the regular space, the time-fibre of the pullback random attractor semi-converges to the random attractor of the autonomous stochastic equation as the time-parameter goes to minus infinity. The general delay force is assumed to be pointwise Lipschitz continuous only, which relaxes the uniform Lipschitz condition in the literature and includes more examples.
In this paper, we are concerned with the dynamics of a diffusive SIRI epidemic model with heterogeneous parameters and distinct dispersal rates for the susceptible and infected individuals. We first establish the basic properties of solutions to the model, and then identify the basic reproduction number
This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have defined sign. In the meantime, we also establish a number of Gagliardo-Nirenberg inequalities in the corresponding Sobolev spaces which will be applicable to other similar situations.
We study a kinetic-fluid model in a
We consider a general inhomogeneous parabolic initial-boundary value problem for a
This note studies the asymptotics of radial global solutions to the non-linear fractional Schrödinger equation
Indeed, using a new method due to Dodson-Murphy [
We consider the conserved phase-field system
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