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Zihua Guo Xingxing Liu Luc Molinet Zhaoyang Yin 《Journal of Differential Equations》2019,266(2-3):1698-1707
We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space and even in the Besov space for . Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5], [14], [16]). 相似文献
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We consider the following system with critical exponent in : where , and . Using finite dimensional reduction method, we prove the existence of multi-bump solutions. Their bumps can be placed on arbitrarily many or even infinitely many lattice points in . Since or , we introduce two new norms to avoid singularity. 相似文献
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We look for positive solutions for the singular equation where , , is a parameter, and has some summability properties. By using a perturbation method and critical point theory, we obtain two solutions when and the parameter is small. 相似文献
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In this paper, we propose a sufficient and necessary condition for the boundedness of all the solutions for the equation with the critical situation that on g and p, where , is periodic and is bounded. 相似文献
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S. Sidi Ahmed G. Dimitri Ngantso M. Boujnah A. Benyoussef A. El Kenz 《Physics letters. A》2019,383(2-3):121-126
By using the density functional theory (DFT) and Monte Carlo simulations (MCS) with the Heisenberg model, we have studied magnetic properties of the bulk perovskite YCrO3. The exchange couplings of the Heisenberg model and the magnetic anisotropy are investigated. The 110 direction in the crystalline structure of the compound has shown the minimum energy, it is the easy magnetic direction. Using Monte Carlo simulations, the magnetizations behavior, the effects of system parameters and the critical exponents of the compound YCrO3 are implemented. It is shown that the bulk perovskite YCrO3 belongs to the 3D Heisenberg universality class. 相似文献
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《Comptes Rendus Chimie》2019,22(5):386-392
Dimeric alkylammonium salts – gemini surfactants – due to their unusual very low critical micelle concentration and minimal inhibitory concentration are subject to intensive research as surface active and antimicrobial compounds. Thanks to the presence of two positively charged nitrogen atoms and a large molecular surface, gemini surfactants are also very efficient corrosion inhibitors. To strengthen the electrostatic adsorption of ammonium cations on a metal surface, which is a key parameter in the inhibition of corrosion, heteroatoms (O, S, N, or P) and π-electron systems can be introduced into the gemini surfactant structure to increase chemical adsorption. In this study, we investigated the relationship between the alkyl chain length and critical micelle concentration for gemini surfactants containing an oxygen atom in the spacer, that is, bis(N-alkyl-N,N-dimethylethylammonium)ether dibromides, for potential use as corrosion inhibitors. 相似文献
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