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1.
《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2021,38(5):1337-1371
In this paper we consider minimizers of the functional where is a bounded open set and where are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets have finite perimeter and that their free boundary is composed of a regular part, which is locally the graph of a -regular function, and a singular part, which is empty if , discrete if and of Hausdorff dimension at most if , for some . 相似文献
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In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method. 相似文献
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Prof. Dr. Carsten Jenne Dr. Mathias Keßler Jonas Warneke 《Chemistry (Weinheim an der Bergstrasse, Germany)》2015,21(15):5887-5891
The acidity of protic cations and neutral molecules has been studied extensively in the gas phase, and the gas‐phase acidity has been established previously as a very useful measure of the intrinsic acidity of neutral and cationic compounds. However, no data for any anionic acids were available prior to this study. The protic anions [H(B12X12)]? (X=F, Cl, Br, I) are expected to be the most acidic anions known to date. Therefore, they were investigated in this study with respect to their ability to protonate neutral molecules in the gas phase by using a combination of mass spectrometry and quantum‐chemical calculations. For the first time it was shown that in the gas phase protic anions are also able to protonate neutral molecules and thus act as Brønsted acids. According to theoretical calculations, [H(B12I12)]? is the most acidic gas‐phase anion, whereas in actual protonation experiments [H(B12Cl12)]? is the most potent gas‐phase acidic anion for the protonation of neutral molecules. This discrepancy is explained by ion pairing and kinetic effects. 相似文献
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Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting. 相似文献
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Florence Drui Emmanuel Franck Philippe Helluy Laurent Navoret 《Comptes Rendus Mecanique》2019,347(3):259-269
The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables. 相似文献
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Dr. Soichiro Ogi Natsumi Fukaya Dr. Arifin Bastian Bjerkem Skjelstad Dr. Yuh Hijikata Prof. Dr. Shigehiro Yamaguchi 《Chemistry (Weinheim an der Bergstrasse, Germany)》2019,25(30):7303-7307
The self-assembly of an amide-functionalized dithienyldiketopyrrolopyrrole (DPP) dye in aqueous media was achieved through seed-initiated supramolecular polymerization. Temperature- and time-dependent studies showed that the spontaneous polymerization of the DPP derivative was temporally delayed upon cooling the monomer solution in a methanol/water mixture. Theoretical calculations revealed that an amide-functionalized DPP derivative adopts an energetically favorable folded conformation in the presence of water molecules due to hydration. This conformational change is most likely responsible for the trapping of monomers in the initial stage of the cooperative supramolecular polymerization in aqueous media. However, the monomeric species can selectively interact with externally added fragmented aggregates as seeds through concerted π-stacking and hydrogen-bonding interactions. Consequently, the time course of the supramolecular polymerization and the morphology of the aggregated state can be controlled, and one-dimensional fibers that exhibit a J-aggregate-like bathochromically shifted absorption band can be obtained. 相似文献