Mathematische Nachrichten最新文献

The Gross–Pitaevskii (GP) equation is a model for the description of the dynamics of Bose–Einstein condensates. Here, we consider the GP equation in a two-dimensional setting with an external periodic potential in the $�x$-direction and a harmonic oscillator potential in the $�y$-direction in the so-called tight-binding limit. We prove error estimates which show that in this limit the original system can be approximated by a discrete nonlinear Schrödinger equation. The paper is a first attempt to generalize the results from [19] obtained in the one-dimensional setting to higher space dimensions and more general interaction potentials. Such a generalization is a non-trivial task due to the oscillations in the external periodic potential which become singular in the tight-binding limit and cause some irregularity of the solutions which are harder to handle in higher space dimensions. To overcome these difficulties, we work in anisotropic Sobolev spaces. Moreover, additional non-resonance conditions have to be satisfied in the two-dimensional case.

First, we introduce a new notion of pseudo-anti commuting for real hypersurfaces in the complex quadric $��Q^m�=�S�O_{�m�+�2�}�/�S�O_m�S�O_2�$ and give a complete classification of Hopf pseudo-Ricci–Yamabe soliton real hypersurfaces in the complex quadric $�Q^m$. Next as an application we obtain a classification of gradient pseudo-Ricci–Yamabe solitons on Hopf real hypersurfaces in $�Q^m$.

In this paper, we discuss the Hyers–Ulam stability of closable (unbounded) operators with some examples. We also present results pertaining to the Hyers–Ulam stability of the sum and product of closable operators to have the Hyers–Ulam stability and the necessary and sufficient conditions of the Schur complement and the quadratic complement of $��2�\times �2�$ block matrix $�A$ in order to have the Hyers–Ulam stability.

We study the existence of positive weak solutions for the following problem:

In this paper, we investigate the stabilization of the transmission problem of the degenerate wave equation and the heat equation under the Coleman–Gurtin heat conduction law or Gurtin–Pipkin law with the memory effect. We investigate the polynomial stability of this system when employing the Coleman–Gurtin heat conduction, establishing a decay rate of type $�t^{�-�4�}$. Next, we demonstrate exponential stability in the case when Gurtin–Pipkin heat conduction is applied.

The work deals with the Ericksen–Leslie system for nematic liquid crystals on the space $�R^N$ with $��N�\ge �3�$. In our work, we suppose the initial condition $�v_0$ stays on an arc connecting two fixed orthogonal vectors on the unit sphere. Thanks to this geometric assumption, we prove through energy a priori estimates the local existence and the global existence for small initial data of a solution

We study a forager–exploiter model with nonlinear diffusions:

We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space $�{\ell }_1$. This is achieved after proving that on the analogous algebra for $�{\ell }_p$, $��1�\le �p�<�\infty �$, the radius function of any evaluation homomorphism $��{\delta }_x�,��x�\in �{\ell }_p�$, coincides with the norm of $�x$.