Some Properties of Solutions to the Novikov Equation with Weak Dissipation Terms

In this paper, we investigate the Novikov equation with weak dissipation terms. First, we give the local well-posedness and the blow-up scenario. Then, we discuss the global existence of the solutions under certain conditions. After that, on condition that the compactly supported initial data keeps its sign, we prove the infinite propagation speed of our solutions, and establish the large time behavior. Finally, we also elaborate the persistence property of our solutions in weighted Sobolev space.     

Invariability of Trivial Extensions of Tilted Algebras Under Stable Equivalences

As a sequel to [8], we investigate here the behaviour of thetrivial extensions of tilted algebras under stable equivalence.It will be shown that if a finite-dimensional symmetric algebra is stably equivalent to the trivial extension of a tilted algebraB, then is the trivial extension of some tilted algebra A whichhas the same type as B.     

Luikov equations applicable to sublimation-drying

Present paper presents a derivation of Luikov equations applicable to sublimation-drying. The physical situation and transfer mechanism are elucidated clearly. The coefficients appearing in Luikov equations are given in a more explicit way. Some formulation mistakes in recent publications are indicated.

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Anwendung der Luikov-Gleichungen auf die Sublimationstrocknung

Zusammenfassung Die Untersuchung bezieht sich auf eine Ableitung der Luikov-Gleichungen, mittels deren sich der Vorgang der Sublimationstrocknung analysieren läßt. Physikalische Anfangssituation und Austauschmechanismen werden klar herausgestellt und die in den Luikov-Gleichungen auftretenden Koeffizienten in expliziter Weise angegeben. Ferner erfolgt Hinweis auf Formulierungsfehler in jüngeren Veröffentlichungen.

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Nomenclature C M _v/V _f, concentration of vapor, kg/m³ - c _pv specific heat of vapor at constant pressure, J/kg K - c _pw specific heat of adsorbed water at constant pressure, J/kg K - c _s specific heat of solid skeleton, J/kg K - C _s M _s/V _f, concentration of solid skeleton, kg/m³ - C _w M _w/V _f, concentration of adsorbed water, kg/m³ - f V _w/V _f, volumetric fraction of adsorbed water - j _F mass flux of vapor by diffusion (Fick) transfer, kg/m² s - j _D mass flux of vapor by filtration (Darcy) transfer, kg/m² s - j _v total mass flux of vapor, kg/m² s - k permeability, m² - M _s mass of solid skeleton, kg - M _v mass of vapor in pores, kg - M _w mass of adsorbed water, kg - P pressure, Pa - q heat flux, W/m² - R gas constant, J/kg K - T temperature, K - V _f volume of the framework of porous medium, m³ - V _v volume of vapor in porous medium, m³ - V _w volume of the absorbed water, m³ Greek symbols /(c _p), effective thermal diffusivity, m²/s - _m effective vapor diffusivity in porous medium, m²/s - _p R T /, Luikov pressure diffusivity, m²/s - +f, porosity of the porous medium - effective thermal conductivity of porous body, W/m K - dynamic viscosity of vapor, kg/m s - kinematic viscosity, m²/s - Ck/=k/, Luikov filtration motion coefficient, s - V _v/V _f, volumetric fraction of vapor - density of absorbed water, kg/m³ - (c _p) M _v c _pv+M _s c _s+M _w c _pw /V _f=Cc _pv+C _s c _s+fc _pw, effective product of density and specific heat of humid porous body, J/m³K     

Variational aspects of the Seiberg-Witten functional

The Seiberg-Witten equations that have recently found important applications for four-dimensional geometry are the Euler-Lagrange equations for a functional involving a connection A on a line bundleL and a section of another bundleW ⁺ constructed fromL and a spinor bundle on a given four-dimensional Riemannian manifold. We show the regularity of weak solutions and the Palais-Smale condition for this functional.