An overdetermined problem for a class of anisotropic equations in a cylindrical domain

2020 ◽  
Vol 43 (9) ◽  
pp. 6117-6125 ◽  
Author(s):  
Luminiţa Barbu ◽  
Adrian Eracle Nicolescu
Keyword(s):  
Cylindrical Domain ◽  
Overdetermined Problem

scholarly journals $L^{p}-L^{q}$-Maximal regularity of the Van Wijngaarden–Eringen equation in a cylindrical domain

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Carlos Lizama ◽  
Marina Murillo-Arcila
Keyword(s):  
Acoustic Waves ◽  
Maximal Regularity ◽  
Bubble Radius ◽  
Fourier Multipliers ◽  
Cylindrical Domain ◽  
Lebesgue Spaces ◽  
Regularity Problem ◽  
Bubbly Liquids

Abstract We consider the maximal regularity problem for a PDE of linear acoustics, named the Van Wijngaarden–Eringen equation, that models the propagation of linear acoustic waves in isothermal bubbly liquids, wherein the bubbles are of uniform radius. If the dimensionless bubble radius is greater than one, we prove that the inhomogeneous version of the Van Wijngaarden–Eringen equation, in a cylindrical domain, admits maximal regularity in Lebesgue spaces. Our methods are based on the theory of operator-valued Fourier multipliers.

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

A new approach to memory and logic-cylindrical domain devices

1969 ◽  
Author(s):  
A. H. Bobeck ◽  
R. F. Fischer ◽  
A. J. Perneski
Keyword(s):  
Cylindrical Domain ◽  
New Approach

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

Cylindrical optimal rearrangement problem leading to a new type obstacle problem

2018 ◽  
Vol 24 (2) ◽  
pp. 859-872 ◽  
Author(s):  
Hayk Mikayelyan
Keyword(s):  
Comparison Principle ◽  
Obstacle Problem ◽  
Normal Derivative ◽  
Force Function ◽  
Cylindrical Domain ◽  
New Type ◽  
Existence And Regularity Results ◽  
Regularity Results ◽  
Cylindrical Axis

An optimal rearrangement problem in a cylindrical domainΩ=D× (0, 1) is considered, under the constraint that the force function does not depend on thexnvariable of the cylindrical axis. This leads to a new type of obstacle problem in the cylindrical domain     Δu(x′,xn) =χ{v>0}(x′) +χ{v=0}(x′) [∂νu(x′,0) +∂νu(x′, 1)]arising from minimization of the functional     ∫Ω½;|∇u(x)|2+χ{v>0}(x′)u(x) dx,wherev(x′) =∫01u(x′,t)dt, and∂νuis the exterior normal derivative ofuat the boundary. Several existence and regularity results are proven and it is shown that the comparison principle does not hold for minimizers.

scholarly journals Entropy Analysis on a Three-Dimensional Wavy Flow of Eyring–Powell Nanofluid: A Comparative Study

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Arshad Riaz ◽  
Ahmed Zeeshan ◽  
M. M. Bhatti
Keyword(s):  
Viscous Dissipation ◽  
Newtonian Fluid ◽  
Entropy Generation ◽  
Pressure Rise ◽  
Software Tool ◽  
Bejan Number ◽  
Mathematical Treatment ◽  
Cylindrical Domain ◽  
Special Cases ◽  
The Impact

The thermal management of a system needs an accurate and efficient measurement of exergy. For optimal performance, entropy should be minimized. This study explores the enhancement of the thermal exchange and entropy in the stream of Eyring–Powell fluid comprising nanoparticles saturating the vertical oriented dual cylindrical domain with uniform thermal conductivity and viscous dissipation effects. A symmetrical sine wave over the walls is used to induce the flow. The mathematical treatment for the conservation laws are described by a set of PDEs, which are, later on, converted to ordinary differential equations by homotopy deformations and then evaluated on the Mathematica software tool. The expression of the pressure rise term has been handled numerically by using numerical integration by Mathematica through the algorithm of the Newton–Cotes formula. The impact of the various factors on velocity, heat, entropy profile, and the Bejan number are elaborated pictorially and tabularly. The entropy generation is enhanced with the variation of viscous dissipation but reduced in the case of the concentration parameter, but viscous dissipation reveals opposite findings for the Newtonian fluid. From the abovementioned detailed discussion, it can be concluded that Eyring–Powell shows the difference in behavior in the entropy generation and in the presence of nanoparticles due to the significant dissipation effects, and also, it travels faster than the viscous fluid. A comparison between the Eyring-Powell and Newtonian fluid are also made for each pertinent parameter through special cases. This study may be applicable for cancer therapy in biomedicine by nanofluid characteristics in various drugs considered as a non-Newtonian fluid.

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