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Start Over Coverage 293-305

1. On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order

Creator:
Amato, Roberto
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, derivace funkce, mathematics, derivatives (mathematics), nonlinear parabolic system, fractional differentiability, spatial derivative, weak solution, 13, and 51
Language:
English
Description:
We are concerned with the problem of differentiability of the derivatives of order m + 1 of solutions to the “nonlinear basic systems” of the type {\left( { - 1} \right)^m}\sum\limits_{\left| \alpha \right| = m} {{D^\alpha }{A^\alpha }\left( {{D^{\left( m \right)}}u} \right)} + \frac{{\partial u}}{{\partial t}} = 0\;in\;Q. We are able to show that {D^\alpha }u \in {L^2}\left( { - a,0,{H^\partial }\left( {B\left( \sigma \right),{\mathbb{R}^N}} \right)} \right),\;\left| \alpha \right| = m + 1, for \partial\in \left ( 0,1/2 \right )and this result suggests that more regularity is not expectable., Roberto Amato., and Obsahuje seznam literatury
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The far-field modelling of transonic compressible flows

Creator:
Coclici, C. A., Sofronov, I. L., and Wendland, W. L.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
artificial boundary and transmission conditions, compressible transonic flow, linearized Euler equations, integral equations with kernels of Cauchy type, potential theory, and domain decomposition
Language:
English
Description:
We present a method for the construction of artificial far-field boundary conditions for two- and three-dimensional exterior compressible viscous flows in aerodynamics. Since at some distance to the surrounded body (e.g. aeroplane, wing section, etc.) the convective forces are strongly dominant over the viscous ones, the viscosity effects are neglected there and the flow is assumed to be inviscid. Accordingly, we consider two different model zones leading to a decomposition of the original flow field into a bounded computational domain (near field) and a complementary outer region (far field). The governing equations as e.g. compressible Navier-Stokes equations are used in the near field, whereas the inviscid far field is modelled by Euler equations linearized about the free-stream flow. By treating the linear model analytically and numerically, we get artificial far-field boundary conditions for the (nonlinear) interior problem. In the two-dimensional case, the linearized Euler model can be handled by using complex analysis. Here, we present a heterogeneous coupling of the above-mentioned models and show some results for the flow around the NACA0012 airfoil. Potential theory is used for the three-dimensional case, leading also to non-local artificial far-field boundary conditions.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public