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21.
Jules K. Djoko Virginie S. Konlack Mohamed Mbehou 《Numerical Methods for Partial Differential Equations》2020,36(1):86-117
In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations. 相似文献
22.
Djamel Ait-Akli & Abdelkader Merakeb 《偏微分方程(英文版)》2020,33(1):64-92
In this paper we consider the Lamé system on a polygonal convex domain
with mixed boundary conditions of Dirichlet-Neumann type. An explicit L2 norm
estimate for the gradient of the solution of this problem is established. This leads to an
explicit bound of the H1 norm of this solution. Note that the obtained upper-bound is
not optimal. 相似文献
23.
24.
Zhichao Zhang 《Mathematical Methods in the Applied Sciences》2020,43(11):6663-6676
Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the Lp-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given. 相似文献
25.
We study the initial–boundary value problem for a Laplace reaction–diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show asymptotic convergence of bounded global solutions if they exist under the assumption that the reaction function is analytic in neighborhoods of their -limit sets. Reduction of degenerate evolution equation to multivalued evolution equation enables us to use the theory of the infinite-dimensional Łojasiewicz–Simon gradient inequality. 相似文献
26.
《Discrete Mathematics》2020,343(4):111696
For a set the -neighbourhood of is , where denotes the usual graph distance on . Harper’s vertex-isoperimetric theorem states that among the subsets of given size, the size of the -neighbourhood is minimised when is taken to be an initial segment of the simplicial order. Aubrun and Szarek asked the following question: if is a subset of given size for which the sizes of both and are minimal for all , does it follow that is isomorphic to an initial segment of the simplicial order?Our aim is to give a counterexample. Surprisingly it turns out that there is no counterexample that is a Hamming ball, meaning a set that lies between two consecutive exact Hamming balls, i.e. a set with for some . We go further to classify all the sets for which the sizes of both and are minimal for all among the subsets of of given size. We also prove that, perhaps surprisingly, if for which the sizes of and are minimal among the subsets of of given size, then the sizes of both and are also minimal for all among the subsets of of given size. Hence the same classification also holds when we only require and to have minimal size among the subsets of given size. 相似文献
27.
Mengjie ZHANG 《数学年刊B辑(英文版)》2022,43(3):425-442
In this paper, the author concerns two trace Trudinger-Moser inequalities and obtains the corresponding extremal functions on a compact Riemann surface (Σ, g) with smooth boundary ?Σ. Explicitly, let λ1(?Σ) = inf u∈W1,2 (Σ,g),R ?Σ udsg=0,u6≡0 R Σ(|?gu|2 + u2 )dvg R ?Σ u2 dsg and H = n u ∈ W1,2 (Σ, g) : Z Σ(|?gu|2 + u2 )dvg ? α Z ?Σ u2dsg ≤ 1 and Z ?Σ u dsg = 0o ,where W1,2 (Σ, g) denotes the usual Sobolev space and ?g stands for the gradient operator.By the method of blow-up analysis, we obtain sup u∈H Z ?Σ e πu2 dsg ( < +∞, 0 ≤ α < λ1(?Σ),= +∞, α ≥ λ1(?Σ).Moreover, the author proves the above supremum is attained by a function uα ∈ H∩C∞(Σ)for any 0 ≤ α < λ1(?Σ). Further, he extends the result to the case of higher order eigenvalues. The results generalize those of [Li, Y. and Liu, P., Moser-Trudinger inequality on the boundary of compact Riemannian surface, Math. Z., 250, 2005, 363–386], [Yang,Y., Moser-Trudinger trace inequalities on a compact Riemannian surface with boundary,Pacific J. Math., 227, 2006, 177–200] and [Yang, Y., Extremal functions for TrudingerMoser inequalities of Adimurthi-Druet type in dimension two, J. Diff. Eq., 258, 2015,3161–3193] 相似文献
28.
29.
The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets. 相似文献
30.
Sabyasachi Kar Yu‐Shu Wang Wei‐Qi Li Xiu‐Dong Sun 《International journal of quantum chemistry》2015,115(22):1573-1579
The effect of plasma screening on the dynamic dipole polarizability (DPP) of two‐electron ions Be2+, B3+, and C4+ has been investigated using highly correlated exponential wave functions within the framework of pseudostate summation technique and Debye screening concept. Plasma‐screening effect on the oscillator strengths (OS) of the ultraviolet and visible series has also been investigated for the systems Li+, Be2+, B3+, C4+. The DPP are reported as functions of screening parameters. The OS for S‐P transitions are also reported for various screening parameters. The OS and dynamic polarizability show interesting behavior with increasing screening strength and nuclear charge. © 2015 Wiley Periodicals, Inc. 相似文献