Search results for "boundary"

Der O2-Austausch zwischen Capillaren und Gewebe I. O2-Konzentrationsprofile in Blutcapillaren und deren Umgebung

1968

The differential equations valid for technical heat exchangers can also describe the O2 exchange in the blood capillaries and the exchange of molecules like THO and acetamid in the renal tubules. Differences in the boundary conditions occur, however. Hence, these differential equations were resolved for the corresponding boundary conditions. The results permit us to conclude that the concentration profiles occurring in the capillaries and renal tubules, as a result of diffusion in the capillary cross-section, can, generally speaking, be disregarded for the following reason: Although the differences in partial pressure between the capillary wall and capillary centre, at the beginning of the …

A model of capillary phenomena in RN with subcritical growth

2020

This paper deals with the nonlinear Dirichlet problem of capillary phenomena involving an equation driven by the p-Laplacian-like di¤erential operator in RN. We prove the existence of at least one nontrivial nonnegative weak solution, when the reaction term satisfies a sub-critical growth condition and the potential term has certain regularities. We apply the energy functional method and weaker compactness conditions.

Monte Carlo Simulations of Surfaces and Interfaces in Materials

1996

Many applications of materials are controlled by their surface and interface properties. In particular, metallic alloys (but also mixed dielectric materials and amorphous polymer blends) are not homogeneously mixed on a microscopic length scale, although they are macroscopically homogeneous. Depending on the preparation of the sample, there exists a heterophase microstructure, with typical domain sizes, e.g. in the 1 to 102 µm range, separated by interfaces between them. The physical properties of such intrinsic interfaces (grain boundaries between small crystallites, antiphase domain boundaries in ordered alloys, Bloch walls in magnetic materials, etc.) are not only an important controllin…

Infinitely many solutions to boundary value problem for fractional differential equations

2018

Variational methods and critical point theorems are used to discuss existence of infinitely many solutions to boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. An example is given to illustrate our result.

Carbonate Platform-Basin Transition in SW Sicily. Implications for the Petroleum Exploration in the Maghrebian Thrust and Fold Belt

2009

Carbonate platform-basin systems of Sicily through the Triassic/Jurassic Boundary: Stratigraphic constraints for the paleogeographic reconstructions.

2004

Late Carnian-Early Norian ammonoids from the GSSP candidate section Pizzo Mondello (Sicani mountain, Sicily).

2012

A small collection of ammonoids from the Upper Triassic Scillato Formation at Pizzo Mondello (Agrigento, Sicily) is studied. The specimens were collected in a framework of a project aimed at providing an integrated high-resolution bio-chronostratigraphic support to the Upper Carnian-Norian magnetostratigraphic scale defined at this site, that is located in an historical area from which G.G. Gemmellaro collected the Upper Triassic of ammonoids monographed at the beginning of the XX century. The specimens from Pizzo Mondello were bed-by-bed sampled and represent the first collection of Upper Triassic ammonoids described from Sicily since Gemmellaro time. Quite several levels of the Pizzo Mond…

Fractional p-Laplacian evolution equations

2016

Abstract In this paper we study the fractional p-Laplacian evolution equation given by u t ( t , x ) = ∫ A 1 | x − y | N + s p | u ( t , y ) − u ( t , x ) | p − 2 ( u ( t , y ) − u ( t , x ) ) d y for  x ∈ Ω ,  t > 0 , 0 s 1 , p ≥ 1 . In a bounded domain Ω we deal with the Dirichlet problem by taking A = R N and u = 0 in R N ∖ Ω , and the Neumann problem by taking A = Ω . We include here the limit case p = 1 that has the extra difficulty of giving a meaning to u ( y ) − u ( x ) | u ( y ) − u ( x ) | when u ( y ) = u ( x ) . We also consider the Cauchy problem in the whole R N by taking A = Ω = R N . We find existence and uniqueness of strong solutions for each of the above mentioned problem…

The Cauchy problem in hybrid metric-Palatini f(X)-gravity

2013

The well-formulation and the well-posedness of the Cauchy problem is discussed for {\it hybrid metric-Palatini gravity}, a recently proposed modified gravitational theory consisting of adding to the Einstein-Hilbert Lagrangian an $f(R)$ term constructed {\it \`{a} la} Palatini. The theory can be recast as a scalar-tensor one predicting the existence of a light long-range scalar field that evades the local Solar System tests and is able to modify galactic and cosmological dynamics, leading to the late-time cosmic acceleration. In this work, adopting generalized harmonic coordinates, we show that the initial value problem can always be {\it well-formulated} and, furthermore, can be {\it well-…

A logarithmic fourth-order parabolic equation and related logarithmic Sobolev inequalities

2006

A logarithmic fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum semiconductor devices. The existence of global-in-time non-negative weak solutions and some regularity results are shown. Furthermore, we prove that the solution converges exponentially fast to its mean value in the ``entropy norm'' and in the Fisher information, using a new optimal logarithmic Sobolev inequality for higher derivatives. In particular, the rate is independent of the solution and the constant depends only on the initial value of the entropy.