scholarly journals Phase transitions in a coupled viscoelastic system with periodic initial-boundary condition: (I) Existence and uniform boundedness

2007 ◽  
Vol 7 (4) ◽  
pp. 825-837 ◽  
Author(s):  
Ming Mei ◽  
◽  
Yau Shu Wong ◽  
Liping Liu ◽  
◽  
...  
Keyword(s):  
Boundary Condition ◽  
Phase Transitions ◽  
Uniform Boundedness ◽  
Initial Boundary ◽  
Viscoelastic System ◽  
Initial Boundary Condition

scholarly journals Linear parabolic equations with venttsel initial boundary conditions

1994 ◽  
Vol 50 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Yi Zeng ◽  
Yousong Luo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Engineering Problem ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Boundary Condition ◽  
Linear Parabolic Equations

The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.

scholarly journals Comparison between analytical, numerical, and experimental results of grouping effects in droplet streams

2017 ◽  
Author(s):  
Norbert Roth ◽  
Hassan Gomaa ◽  
Alon Livne ◽  
David Katoshevski ◽  
Bernhard Weigand
Keyword(s):  
Numerical Simulation ◽  
Boundary Condition ◽  
Direct Numerical Simulation ◽  
Initial Boundary ◽  
Experimental Results ◽  
Controllable System ◽  
Initial Boundary Condition ◽  
Linear Behaviour ◽  
Monodisperse Droplet ◽  
Monodisperse Droplets

Grouping of droplets was studied in monodisperse droplet streams. This very controllable system allows to studybasic effects. In experiments droplet streams with monodisperse droplets were generated, however, with initially two different inter droplet spacing. A larger inter droplet spacing is followed by a little bit smaller one, which is followed by a larger one and so on. Due to this initial boundary condition groups of two droplets form, which approach each other and finally coagulate. It was found, that the velocity of the droplet approach is linearly dependent on the spacing between the droplets. This process was simulated by direct numerical simulation using the in-house code FS3D. The results of the simulations show the  ame linear behaviour. For larger computational domains thenumerical results approach the experimental results.DOI: http://dx.doi.org/10.4995/ILASS2017.2017.4685

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

Trajectory Generation From Paths for Autonomous Ground Vehicles

2020 ◽  
Author(s):  
Letian Lin ◽  
J. Jim Zhu
Keyword(s):  
Phase Plane ◽  
Longitudinal Velocity ◽  
Initial Boundary ◽  
Limit Function ◽  
Ground Vehicles ◽  
Reverse Time ◽  
Dynamic Constraints ◽  
Autonomous Ground Vehicles ◽  
Practical Concern ◽  
Initial Boundary Condition

Abstract Path-to-trajectory conversion problem for car-like autonomous ground vehicles has been studied in various ways. It is challenging to generate a trajectory which is dynamically feasible for the vehicle and comfortable for the passengers. An important practical concern of low computational costs makes the problem even more difficult. In this work, a path-to-trajectory converter is developed using a novel receding-horizon type suboptimal algorithm. By transforming the dynamic constraints to a longitudinal velocity limit function in the velocity-acceleration phase plane, a time-sub-optimal trajectory satisfying the dynamic constraints and the initial boundary condition is generated by computing the maximum constant acceleration in the down-range horizon. The portion of the trajectory approaching the end of the path is generated in reverse time. As illustrated by some simulation results and validation on a full-scale Kia Soul EV, the proposed path-to-trajectory conversion algorithm is able to account for dynamic constraints of the vehicle and guarantees passenger comfort.

scholarly journals On the evolution of solutions of Burgers equation on the positive quarter-plane

2019 ◽  
Vol 52 (1) ◽  
pp. 237-248
Author(s):  
Esen Hanaç
Keyword(s):  
Boundary Condition ◽  
Analytic Solution ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Condition ◽  
Quarter Plane ◽  
Initial Boundary Value ◽  
Good Agreement

AbstractIn this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; $\matrix{ {{v_t} + v{v_x} - {v_{xx}} = 0,\,\,\,x > 0,\,\,\,t > 0,} \cr {v\left( {x,0} \right) = {u_ + },\,\,\,x > 0,} \cr {v\left( {0,t} \right) = {u_b},\,\,t > 0,} \cr }$ where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

Comparison of the Structures of a Perturbed and Unperturbed Boundary Layer of the Same Reynolds Number

Volume 1 ◽  
2004 ◽  
Author(s):  
O. Oyewola
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Porous Wall ◽  
Initial Boundary ◽  
Reynolds Stresses ◽  
Mean Velocity ◽  
Streamwise Location ◽  
Initial Boundary Condition ◽  
The Difference ◽  
Made In

The comparison of the structures of the boundary layer with and without suction of the same momentum thickness Reynolds number Rθ have been made in a turbulent boundary subjected to concentrated suction, applied through a short porous wall strip. The results indicate that, relative to σ = 0, the mean velocity collapses reasonably well but there are some discrepancies in the Reynolds stresses distributions. These discrepancies are also noted in the distributions of the anisotropy invariant tensor, skewness and flatness factors. The result would suggest that the differences are a result of the difference in the initial boundary condition, which influences the flow structures to a significant streamwise location.

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