Extinction and Non-extinction of Solutions to a Fast Diffusion p-Laplace Equation with Logarithmic Non-linearity

This paper deals with a class of fast diffusion p-Laplace equation with logarithmic non-linearity in a bounded smooth domain with homogeneous Dirichlet boundary condition. By using energy estimates and some ordinary differential inequalities, we study the conditions on extinction and non-extinction of global solutions. The results of this paper extend and complete the previous studies on this equation.

     

On the Stability of a Degenerate Wave Equation Under Fractional Feedbacks Acting on the Degenerate Boundary

Journal of Dynamical and Control Systems - In this work, we are concerned with the study of stabilization of one-dimensional weakly degenerate wave equation utt ? (xγux)x = 0 with x...     

Analysis of pressure and heat distribution in a dilating or contracting filter chamber with two outlets using multivariate spectral quasilinearization method

The development of efficient filters is an essential part of industrial machinery design, specifically to increase the lifespan of a machine. In the filter chamber design considered in this study, the magnetic material is placed along the horizontal surface of the filter chamber. The inside of the filter chamber is layered with a porous material to restrict the outflow of unwanted particles. This study aims to investigate the flow, pressure, and heat distribution in a dilating or contracting filter chamber with two outlets driven by injection through a permeable surface. The proposed model of the fluid dynamics within the filter chamber follows the conservation equations in the form of partial differential equations. The model equations are further reduced to a steady case through Lie's symmetry group of transformation. They are then solved using a multivariate spectral-based quasilinearization method on the Chebyshev–Gauss–Lobatto nodes. Insights and analyses of the thermophysical parameters that drive optimal outflow during the filtration process are provided through the graphs of the numerical solutions of the differential equations. We find, among other results, that expansion of the filter chamber leads to an overall decrease in internal pressure and an increase in heat distribution inside the filter chamber. The results also show that shrinking the filter chamber increases the internal momentum inside the filter, which leads to more outflow of filtrates.     

A numerical study on nonlinear DPL model for analyzing heat transfer in tissue during thermal therapy

In the present paper, therapeutic treatment of infected tumorous cells has been studied through mathematical modeling and simulation of heat transfer in tissues by using a nonlinear dual-phase lag bioheat transfer model with Dirichlet boundary condition. The components of volumetric heat source in this model such as blood perfusion and metabolism are assumed experimentally validated temperature-dependent function, which gives more accurate temperature distribution in tissues through this model. We have used the finite difference and RK (4, 5) techniques of numerical methods to solve the proposed problem and obtained the exact solution in a particular case. After comparison, we got a good agreement between them. We have used dimensionless quantities throughout this paper. The effect of relaxation and thermalization time with respect to dimensionless temperature distribution has been analyzed in the treatment process.     

Influence of radiation and viscous dissipation on MHD heat transfer Casson nanofluid flow along a nonlinear stretching surface with chemical reaction

The present article investigates the influence of Joule heating and chemical reaction on magneto Casson nanofluid phenomena in the occurrence of thermal radiation through a porous inclined stretching sheet. Consideration is extended to heat absorption/generation and viscous dissipation. The governing partial differential equations were transformed into nonlinear ordinary differential equations and numerically solved using the Implicit Finite Difference technique. The article analyses the effect of various physical flow parameters on velocity, heat, and mass transfer distributions. For the various involved parameters, the graphical and numerical outcomes are established. The analysis reveals that the enhancement of the radiation parameter increases the temperature and the chemical reaction parameter decreases the concentration profile. The empirical data presented were compared with previously published findings.     

Hall current effects on MHD flow of chemically reacting fluid through a porous medium with heat source

We considered the magnetohydrodynamic (MHD) free convective flow of an incompressible electrically conducting viscous fluid past an infinite vertical permeable porous plate with a uniform transverse magnetic field, heat source and chemical reaction in a rotating frame taking Hall current effects into account. The momentum equations for the fluid flow during absorbent medium are controlled by the Brinkman model. Through the undisturbed state, both the plate and fluid are in a rigid body rotation by the uniform angular velocity perpendicular to an infinite vertical plate. The perpendicular surface is subject to the homogeneous invariable suction at a right angle to it and the heat on the surface varies about a non-zero unvarying average whereas the warmth of complimentary flow is invariable. The systematic solutions of the velocity, temperature, and concentration distributions are acquired systematically by utilizing the perturbation method. The velocity expressions consist of steady-state and fluctuating situations. It is revealed that the steady part of the velocity field has a three-layer characteristic while the oscillatory part of the fluid field exhibits a multi-layer characteristic. The influence of various governing flow parameters on the velocity, temperature, and concentration are analyzed graphically. We also discuss computational results for the skin friction, Nusselt number, and Sherwood number in the tabular forms.     

Dufour and Soret influence on MHD boundary layer flow of a Maxwell fluid over a stretching sheet with nanoparticles

An analysis has been carried out to examine the heat and mass transfer properties of a two-dimensional incompressible electrically conducting Maxwell fluid over a stretching sheet in the existence of Soret, Dufour, and nanoparticles. In many practical scenarios, such as the polymer extrusion process, the problem presented here is crucial. The flow is examined in terms of the impacts of magnetohydrodynamics and elasticity. Brownian motion and thermophoresis are incorporated into the transport equations. Using adequate similarity variables, the governing partial differential equations and related boundary conditions are non-dimensionalized. The fourth–fifth-order Runge–Kutta–Fehlberg procedure is utilized to solve the consequent transformed ordinary differential equations. The effects of various embedded thermo-physical parameters on the fluid velocity, temperature, concentration, Nusselt number, and Sherwood number have been determined and discussed quantitatively. A comparison of a special case of our results with the one previously reported in the literature shows a very good agreement. An increase in the values of Du and Sr leads to an increase in the temperature and concentration distribution. Nusselt number estimates decrease as Nb estimations increase. Furthermore, this study leads to the study of different flows of electrically conducting fluid over a stretching sheet problem that includes the two-dimensional nonlinear boundary equations.     

高面板坝全寿命周期变形控制方法及应用

高面板坝的变形对面板的安全运行有着特别重要的影响，国内外已建的高面板坝工程中，因坝体变形大导致防渗面板挤压破损，坝体渗漏量大的实例较多，不得不降低水库水位进行修复处理，造成较大的经济损失乃至给大坝的长期运行留下安全隐患。通过发生挤压破损的实例分析，发现变形控制缺乏系统性是发生面板挤压破损的主要因素，为预防面板破损，系统提出了“控制坝体总变形，转化有害变形，适应纵向变形”的坝体变形控制方法，并在使用软硬岩混合料筑坝的董箐面板堆石坝中得到的应用，取得了良好效果，该工程运行至今达十余年，未见面板有挤压破损迹象，该方法对建设200 m以上乃至300 m级超高面板坝具有重要借鉴意义。