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81.
Well‐posedness of initial boundary value problems on longitudinal impact on a composite linear viscoelastic bar 下载免费PDF全文
Akbar B. Aliev Elkhan H. Mammadhasanov 《Mathematical Methods in the Applied Sciences》2017,40(14):5380-5390
We investigate the correctness of the initial boundary value problem of longitudinal impact on a piecewise‐homogeneous semi‐infinite bar consisting of a semi‐infinite elastic part and finite length visco‐elastic part whose hereditary properties are described by linear integral relations with an arbitrary difference kernel. Introducing nonstationary regularization in boundary conditions and in the contact conditions, the well‐posedness of the considered problem is proved. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
82.
General decay of solutions of a wave equation with memory term and acoustic boundary condition 下载免费PDF全文
In this paper, the global solvability to the mixed problem involving the wave equation with memory term and acoustic boundary conditions for non‐locally reacting boundary is considered. Moreover, the general decay of the energy functionality is established by the techniques of Messaoudi. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
83.
The existence of a positive solution for nonlinear fractional differential equations with integral boundary value conditions 下载免费PDF全文
Alberto Cabada Sladjana Dimitrijevic Tatjana Tomovic Suzana Aleksic 《Mathematical Methods in the Applied Sciences》2017,40(6):1880-1891
In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem where 0≤λ < 1,CDα is the Caputo's differential operator of order α, and f:[0,1] × [0,∞)→[0,∞) is a continuous function. Using some cone theoretic techniques, we deduce a general existence theorem for this problem. Then, we consider two following more general problems for arbitrary α, 1≤n < α≤n + 1: Problem 1: where , 0≤λ < k + 1; Problem 2: where 0≤λ≤α and Dα is the Riemann–Liouville fractional derivative of order α. For these problems, we give existence results, which improve recent results in the literature. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
84.
A new variant of the Adaptive Cross Approximation (ACA) for approximation of dense block matrices is presented. This algorithm can be applied to matrices arising from the Boundary Element Methods (BEM) for elliptic or Maxwell systems of partial differential equations. The usual interpolation property of the ACA is generalised for the matrix valued case. Some numerical examples demonstrate the efficiency of the new method. The main example will be the electromagnetic scattering problem, that is, the exterior boundary value problem for the Maxwell system. Here, we will show that the matrix valued ACA method works well for high order BEM, and the corresponding high rate of convergence is preserved. Another example shows the efficiency of the new method in comparison with the standard technique, whilst approximating the smoothed version of the matrix valued fundamental solution of the time harmonic Maxwell system. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
85.
On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a‐priori estimates and stability 下载免费PDF全文
Victor A. Kovtunenko Anna V. Zubkova 《Mathematical Methods in the Applied Sciences》2017,40(6):2284-2299
In this paper, we consider the strongly nonlinear Nernst–Planck equations coupled with the quasi‐linear Poisson equation under inhomogeneous, moreover, nonlinear boundary conditions. This system describes joint multi‐component electrokinetics in a pore phase. The system is supplemented by the force balance and by the volume and positivity constraints. We establish well‐posedness of the problem in the variational setting. Namely, we prove the existence theorem supported by the energy and the entropy a‐priori estimates, and we provide the Lyapunov stability of the solution as well as its uniqueness in special cases. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
86.
Exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions 下载免费PDF全文
Yue Wang Günter Leugering Tatsien Li 《Mathematical Methods in the Applied Sciences》2017,40(10):3808-3820
By equivalently replacing the dynamical boundary condition by a kind of nonlocal boundary conditions, and noting a hidden regularity of solution on the boundary with a dynamical boundary condition, a constructive method with modular structure is used to get the local exact boundary controllability for 1‐D quasilinear wave equations with dynamical boundary conditions. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
87.
Heng Li Yongzhi Xu Jian‐Rong Zhou 《Mathematical Methods in the Applied Sciences》2017,40(10):3566-3579
Ductal carcinoma in situ – a special cancer – is confined within the breast ductal only. We derive the mathematical ductal carcinoma in situ model in a form of a nonlinear parabolic equation with initial, boundary, and free boundary conditions. Existence, uniqueness, and stability of problem are proved. Algorithm and illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
88.
This paper is concerned with the problem of heat conduction from an inclusion in a heat transfer layered medium. Making use of the boundary integral equation method, the well-posedness of the forward problem is established by the Fredholm theory. Then an inverse boundary value problem, i.e. identifying the inclusion from the measurements of the temperature and heat flux on the accessible exterior boundary of the medium is considered in the framework of the linear sampling method. Based on a careful analysis of the Dirichlet-to-Neumann map, the mathematical fundamentals of the linear sampling method for reconstructing the inclusion are proved rigorously. 相似文献
89.
《Journal of separation science》2017,40(3):789-797
A common drawback of paper‐based separation devices is their poor detection limit. In this study, we combined field‐amplified sample stacking with moving reaction boundary electrophoresis on a paper chip with six array channels for the parallel separation and concentration of multiple samples. With a new hyphenated technique, the brown I2 from the Fe3+/I− oxidation–reduction reaction emerged near the boundary between the dilute ethylene diamine tetraacetic acid and potassium iodide and highly concentrated KCl solutions. For the separation and concentration of three components, Cr3+, Cu2+, and Fe3+, the Fe3+ detection limit was improved at least 266‐fold by comparing the hyphenated technique with moving reaction boundary electrophoresis. The detection limit of Fe3+ was found to be as low as 0.34 ng (20 μM) on the paper chip. We also demonstrated the analysis of a real sample of four metal ions, with detection limits as follows: 0.16 μg Cr3+, 1.5 μg Ni2+, 0.64 μg Cu2+, and 1.5 μg Co2+. The synergy of field‐amplified sample stacking and moving reaction boundary electrophoresis in the micron paper‐based array channels dramatically improved the detection limit and throughput of paper‐based electrophoresis. 相似文献
90.
Florian Beyer 《偏微分方程通讯》2017,42(8):1199-1248
We consider self-gravitating fluids in cosmological spacetimes with Gowdy symmetry on the torus T3 and, in this class, we solve the singular initial value problem for the Einstein–Euler system of general relativity, when an initial data set is prescribed on the hypersurface of singularity. We specify initial conditions for the geometric and matter variables and identify the asymptotic behavior of these variables near the cosmological singularity. Our analysis of this class of nonlinear and singular partial differential equations exhibits a condition on the sound speed, which leads us to the notion of sub-critical, critical, and super-critical regimes. Solutions to the Einstein–Euler systems when the fluid is governed by a linear equation of state are constructed in the first two regimes, while additional difficulties arise in the latter one. All previous studies on inhomogeneous spacetimes concerned vacuum cosmological spacetimes only. 相似文献