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Existence and Uniqueness of Solution for a Class of Nonlinear Degenerate Elliptic Equations 下载免费PDF全文
Albo Carlos Cavalheiro 《分析论及其应用》2020,36(1):69-88
In this work we are interested in the existence and uniqueness of solutions for the Navier problem associated to the degenerate nonlinear elliptic equations■,in the setting of the weighted Sobolev spaces. 相似文献
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Weiliang Xiao & Xuhuan Zhou 《数学研究》2020,53(3):316-328
We study a kind of generalized porous medium equation with fractional Laplacian and abstract pressure term. For a large class of equations corresponding to the form: $u_t+\nu \Lambda^{\beta}u=\nabla\cdot(u\nabla Pu)$, we get their local well-posedness in Fourier-Besov spaces for large initial data. If the initial data is small, then the solution becomes global. Furthermore, we prove a blowup criterion for the solutions. 相似文献
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The Swendsen‐Wang (SW) dynamics is a popular Markov chain for sampling from the Gibbs distribution for the ferromagnetic Ising model on a graph G = (V,E). The dynamics is conjectured to converge to equilibrium in O(|V|1/4) steps at any (inverse) temperature β, yet there are few results providing o(|V|) upper bounds. We prove fast convergence of the SW dynamics on general graphs in the tree uniqueness region. In particular, when β < βc(d) where βc(d) denotes the uniqueness/nonuniqueness threshold on infinite d‐regular trees, we prove that the relaxation time (i.e., the inverse spectral gap) of the SW dynamics is Θ(1) on any graph of maximum degree d ≥ 3. Our proof utilizes a monotone version of the SW dynamics which only updates isolated vertices. We establish that this variant of the SW dynamics has mixing time and relaxation time Θ(1) on any graph of maximum degree d for all β < βc(d). Our proof technology can be applied to general monotone Markov chains, including for example the heat‐bath block dynamics, for which we obtain new tight mixing time bounds. 相似文献
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Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients 下载免费PDF全文
Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
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The in vitro protein digestibility (IVPD) of napin was studied using different pretreatment methods, including ultrasound, mixing napin with lactalbumin, and ultrasound-assisted protein mixing. The relationships between IVPD, molecular structure, and disulfide bonds were explored, showing that the IVPD of napin was the highest compared with the control when treated with 40% ultrasound power. When the proportion of napin to lactalbumin was 5:5, a synergistic influence between the two proteins was observed. Further investigation showed that the IVPD of napin was clearly improved by treatment with ultrasound-assisted protein mixing. Compared with the single protein in the control, the β-sheet content in the secondary structure of the mixed protein after sonication was reduced from 45.02% to 37.16%. The ordered protein structure was also disrupted by ultrasound, as supported by fluorescence intensity and surface hydrophobicity analyses. The decreased number of disulfide bonds and conformational changes indicated that the IVPD of rapeseed napin was closely related to the disulfide bond content. This study provides a theoretical basis for improving protein digestibility by combining ultrasound with physical mixing. 相似文献
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Stability of Viscoelastic Wave Equation with Structural $\delta$-Evolution in $\mathbb{R}^{n}$ 下载免费PDF全文
The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structural $\delta$-evolution models. By using the energy method in the Fourier spaces, we obtain the decay estimates of the solution to considered problem. 相似文献
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In an aim to prove the efficiency of polyphenols of Rosa canina fruits in promoting human health. A methanolic extract of R. canina fruits was prepared by successive maceration with solvents of increasing polarity. The polyphenol composition was analyzed by HPLC–DAD–ESI–MS. The biological activity of this extract on SH-SY5Y cells and HepG2 cells was then studied. The antioxidant activity was tested by various in vitro tests such as DPPH-radical-scavenging activity, FRAP assay, hydroxyl radical scavenging assay and total antioxidant capacity. The subacute toxicity of R. canina was tested on female rats by repeated intraperitoneal administration of various doses. The phenolic profiles showed 25 antioxidants distributed into three classes of phenolic compounds: glycosylated and agglomerated flavonoids/isoflavonoids, tannins and phenanthrenes. Qualitative phytochemical analyses showed that this extract lacks alkaloids. The methanolic extract of R. canina fruits has a total antioxidant capacity of 82.69 ± 1.18 μg EAA/mg of methanol extract and the IC50 of the methods used is in the following increasing order: FRAP assay (61.88 μg/ml), then hydroxyl radical scavenging assay (67.45 μg/ml) and then DPPH radical-scavenging activity (129.81 μg/ml). The extract of R. canina did not cause any phenotypic signs of toxicity or mortality during and after treatment. The LD50 was >5,000 mg/kg, hence, R. canina was considered nontoxic. An in vivo study proved the protective effect of R. canina against cardiac and hepato-renal toxicities. These results drew the importance of a healthy diet, where diets rich in R. canina fruits can be used as a rich natural source of antioxidants and anticarcinogenic phenolic compounds. 相似文献
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