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Non-negative solutions of generalized porous medium equations.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1986)

Revista Matemática Iberoamericana

The purpose of this paper is to study nonnegative solutions u of the nonlinear evolution equations∂u/∂t = Δφ(u),  x ∈ Rn, 0 < t < T ≤ +∞  (1.1)Here the nonlinearity φ is assumed to be continuous, increasing with φ(0) = 0. This equation arises in various physical problems, and specializing φ leads to models for nonlinear filtrations, or for the gas flow in a porous medium. For a recent survey in these equations see [9].The main object of this work is to study the initial value problem...

Non-negative solutions to fast diffusions.

Bjorn E. J. Dahlberg, Carlos E. Kenig (1988)

Revista Matemática Iberoamericana

The purpose of this work is to study the class of non-negative continuous weak solutions of the non-linear evolution equation∂u/∂t = ∆φ(u),   x ∈ Rn, 0 < t < T ≤ +∞.

Non-Newtonian fluids and function spaces

Růžička, Michael, Diening, Lars (2007)

Nonlinear Analysis, Function Spaces and Applications

In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted N -functions that are used in the studies of generalized Newtonian fluids and problems with p -structure.

Non-parallel plane Rayleigh Benard convection in cylindrical geometry

A. Golbabai (1995)

Applicationes Mathematicae

This paper considers the effect of a perturbed wall in regard to the classical Benard convection problem in which the lower rigid surface is of the form z = ε 2 g ( s ) , s=ε r, in axisymmetric cylindrical polar coordinates (r,ϕ,z). The boundary conditions at s=0 for the linear amplitude equation are found and it is shown that these conditions are different from those which apply to the nonlinear problem investigated by Brown and Stewartson [1], representing the distribution of convection cells near the center....

Non-uniqueness of almost unidirectional inviscid compressible flow

Pavel Šolín, Karel Segeth (2004)

Applications of Mathematics

Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with...

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