Communications on Pure and Applied Analysis
April 2022 , Volume 21 , Issue 4
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In the perfect conductivity problem arising from composites, the electric field may become arbitrarily large as
We consider a Gierer-Meinhardt system on a surface coupled with a parabolic PDE in the bulk, the domain confined by this surface. Such a model was recently proposed and analyzed for two-dimensional bulk domains by Gomez, Ward and Wei (SIAM J. Appl. Dyn. Syst. 18, 2019). We prove the well-posedness of the bulk-surface system in arbitrary space dimensions and show that solutions remain uniformly bounded in parabolic Hölder spaces for all times. The cytosolic diffusion is typically much larger than the lateral diffusion on the membrane. This motivates to a corresponding asymptotic reduction, which consists of a nonlocal system on the membrane. We prove the convergence of solutions of the full system towards unique solutions of the reduction.
In this paper, we study the following fractional Schrödinger-Poiss-on system
In this paper we study the three-marginal optimal mass transportation problem for the Coulomb cost on the plane
We study the Cauchy problem for the surface quasi-geostrophic equation with the critical dissipation in the two dimensional half space under the homogeneous Dirichlet boundary condition. We show the global existence, the uniqueness and the analyticity of solutions, and the real analyticity up to the boundary is obtained. We will show a natural ways to estimate the nonlinear term for functions satisfying the Dirichlet boundary condition.
We consider the semi-relativistic Hartree equation with combined Hartree-type nonlinearities given by
This paper introduce a novel optimization procedure to reduce mixture of Gaussian and impulse noise from images. This technique exploits a non-convex PDE-constrained characterized by a fractional-order operator. The used non-convex term facilitated the impulse component approximation controlled by a spatial parameter
We give a general theory on well-posedness and time asymptotics for growth fragmentation equations in
In this paper we consider the critical quasilinear Schrödinger-Poisson system
In this paper we prove, using a duality method, existence of solutions for the nonlinear elliptic mean field games type system
under different assumptions on
In this paper, the periodic solution and extinction in a periodic chemostat model with delay in microorganism growth are investigated. The positivity and ultimate boundedness of solutions are firstly obtained. Next, the necessary and sufficient conditions on the existence of positive
We study the regularity properties of the second order linear operator in
In this paper we consider the linear quasi-periodic system
In this paper, we consider a homogeneous Neumann initial-boundary value problem (IBVP) for the following two-species and two-stimuli chemotaxis model with both paracrine and autocrine loops:
We consider ground states of the following time-independent nonlinear
The parametric estimation of drift parameter for distribution - dependent stochastic differential delay equations with a small diffusion is presented. The principle technique of our investigation is to construct an appropriate contrast function and carry out a limiting type of argument to show the consistency and convergence rate of the least squares estimator of the drift parameter via interacting particle systems. In addition, two examples are constructed to demonstrate the effectiveness of our work.
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