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Start Over Coverage 273-286

1. Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation

Creator:
Park, Jong Yeoul and Park, Sun Hye
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
asymptotic stability, viscoelastic problems, boundary dissipation, and wave equation
Language:
English
Description:
We consider the damped semilinear viscoelastic wave equation \[ u^{\prime \prime } - \Delta u + \int ^t_0 h (t-\tau ) \div \lbrace a \nabla u(\tau ) \rbrace \mathrm{d}\tau + g(u^{\prime }) = 0 \quad \text{in}\hspace{5.0pt}\Omega \times (0,\infty ) \] with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The Limit Deposit Velocity model, a new approach

Creator:
Miedema, Sape A. and Ramsdell, Robert C.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
critical velocity, Limit Deposit Velocity, slurry transport, and Newtonian fluid
Language:
Slovak
Description:
In slurry transport of settling slurries in Newtonian fluids, it is often stated that one should apply a line speed above a critical velocity, because blow this critical velocity there is the danger of plugging the line. There are many definitions and names for this critical velocity. It is referred to as the velocity where a bed starts sliding or the velocity above which there is no stationary bed or sliding bed. Others use the velocity where the hydraulic gradient is at a minimum, because of the minimum energy consumption. Most models from literature are one term one equation models, based on the idea that the critical velocity can be explained that way. Here the following definition is used: The critical velocity is the line speed below which there may be either a stationary bed or a sliding bed, depending on the particle diameter and the pipe diameter, but above which no bed (stationary or sliding) exists, the Limit Deposit Velocity (LDV). The way of determining the LDV depends on the particle size, where 5 regions are distinguished. These regions for sand and gravel are roughly; very small particles up to 0.014-0.040 mm (d < δv), small particles from δv-0.2 mm, medium particles in a transition region from 0.2-2.00 mm, large particles > 2 mm and very large particles > 0.015·Dp. The lower limit of the LDV is the transition between a sliding bed and heterogeneous transport. The new model is partly based on physics and correlates well with experiments from literature.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public