Communications on Pure and Applied Analysis
December 2020 , Volume 19 , Issue 12
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In this paper, we first study the strong Birkhoff Ergodic Theorem for subharmonic functions with the Brjuno-Rüssmann shift on the Torus. Then, we apply it to prove the large deviation theorems for the finite scale Dirichlet determinants of quasi-periodic analytic Jacobi operators with this frequency. It shows that the Brjuno-Rüssmann function, which reflects the irrationality of the frequency, plays the key role in these theorems via the smallest deviation. At last, as an application, we obtain a distribution of the eigenvalues of the Jacobi operators with Dirichlet boundary conditions, which also depends on the smallest deviation, essentially on the irrationality of the frequency.
In this paper, we are concerned with 3D tamed Navier-Stokes equations with periodic boundary conditions, which can be viewed as an approximation of the classical 3D Navier-Stokes equations. We show that the strong solution of 3D tamed Navier-Stokes equations driven by Poisson random measure converges weakly to the strong solution of 3D tamed Navier-Stokes equations driven by Gaussian noise on the state space
This article is concerned with the limiting behavior of dynamics of a class of non-autonomous stochastic partial differential equations driven by colored noise on unbounded thin domains. We first prove the existence of tempered pullback random attractors for the equations defined on
We study two-dimensional semilinear strongly damped wave equation with mixed nonlinearity
This work concerns the distributional solutions of a conformally invariant system of
We consider the low regularity behavior of the fourth order cubic nonlinear Schrödinger equation (4NLS)
In this article we investigate the possible losses of regularity of the solution for hyperbolic boundary value problems defined in the strip
This question has already been widely studied in the half-space geometry in which a full characterization is almost completed (see [
Crudely speaking the question addressed here is "can several boundaries make the situation becomes worse?".
Here we focus our attention to one special case of loss (namely the elliptic degeneracy of [
In this paper, we study evolution equation
In this paper we prove structural and topological characterizations of the screened Sobolev spaces with screening functions bounded below and above by positive constants. We generalize a method of interpolation to the case of seminormed spaces. This method, which we call the truncated method, generates the screened Sobolev subfamily and a more general screened Besov scale. We then prove that the screened Besov spaces are equivalent to the sum of a Lebesgue space and a homogeneous Sobolev space and provide a Littlewood-Paley frequency space characterization.
In this article, several systems of equations which model surface water waves generated by a sudden bottom deformation (bump) are studied. Because the effect of such deformation are often approximated by assuming the initial water surface has a deformation (bucket), this procedure is investigated and we prove rigorously that by using the correct bucket, the solutions of the regularized bump problems converge to the solution of the bucket problem.
This paper deals with a fourth order parabolic PDE arising in the theory of epitaxial growth, which was studied in [
This paper deals with the system with linearly coupled of nonlocal problem with critical exponent,
In this article, we study a reaction-diffusion model on infinite spatial domain for two competing biological species (
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