We study the Dirichlet problem for the pseudoparabolic equation perturbed with the -Laplacian diffusion term,
We study the Dirichlet problem for the pseudoparabolic equation perturbed with the -Laplacian diffusion term,
We study the smoothness of the topological equivalence between a linear equation and its unbounded nonlinear perturbation. To the best of our knowledge, without using spectral bound conditions, such a study has not been previously considered in the literature. The main result of this work fills in this gap. It shows on the positive half line that this kind of topological equivalence is of class when the linear part is a uniform contraction and the nonlinearities considered are unbounded with respect to the space variable.
The expression for the Weyl–Titchmarsh function is presented for skew-self-adjoint Dirac systems with rectangular potentials. As a specific application of this expression, we provide a new proof of the celebrated local Borg–Marchenko uniqueness theorem. Furthermore, we establish the high-energy asymptotic expansion of the Weyl function and the local uniqueness theorem for locally smooth potentials at the right endpoint.
In this paper, we establish the sharp criteria for the existence and the nonexistence of negative solutions of the following -Hessian inequality with a nonlocal term:
A new operator for certain types of ultrametric Cantor sets is constructed using the measure coming from the spectral triple associated with the Cantor set, as well as its zeta function. Under certain mild conditions on that measure, it is shown that it is an integral operator similar to the Vladimirov–Taibleson operator on the -adic integers. Its spectral properties are studied, and the Markov property and kernel representation of the heat kernel generated by this so-called Vladimirov–Pearson operator is shown, viewed as acting on a certain Sobolev space. A large class of these operators have a heat kernel and a Green function explicitly given by the ultrametric wavelets on the Cantor set, which are eigenfunctions of the operator.
This paper studies stability of solutions for the 3D generalized incompressible Hall-MHD Megnetohydrodynamics equations in the periodic domain with the magnetic field near a nontrivial equilibrium. Some new observations and estimates are implemented to exploit the enhanced dissipation produced by the nontrivial background magnetic field, which satisfies the Diophantine condition. Global stability and explicit time decay rates of solutions are shown.
Metaplectic operators form a relevant class of operators appearing in different applications, in this work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off-diagonal decay conditions, and quasi-diagonality by imposing the same conditions on the smoothing of the kernel through convolution with the Gaussian. Kernels of metaplectic operators are not diagonal. Nevertheless, as we shall prove, they are quasi-diagonal under suitable conditions. Motivation for our study comes from problems in time–frequency analysis, that we discuss in the last section.
We introduce the Hardy spaces with in the new weights , , associated with the Bessel operator
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