Errata

It is a pleasure to thank Professors R. K. Kaul and T. A. Palka for helping to bring these matters to my attention, and for their useful comments on my previous papers.     

The spectrum of small perturbations in plane couette-poiseuille flow

The spectrum of small perturbations of plane Couette-Poiseuille flow is studied. The perturbations are classified according to their behavior at large wave numbers. The changes in the spectrum are traced as the transition is made from Poiseuille to Couette flow at fixed Reynolds number. The behavior of the perturbations is considered as a function of the Reynolds number.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 63–67, March–April, 1971.The author wishes to thank M. A. Gol'dshtik for his attention to the paper, V. A. Sapozhnikov for useful discussions, and V. N. Shtern for his great assistance and help with the paper and for useful discussions.     

Self-oscillational motion of a cylinder towed in weak aqueous polymer solution

A study is made of the effect of polymer additions on the nonstationary vibrational motion of a cylinder towed in a weak aqueous solution of the polymer and capable of making transverse displacements under the action of the force arising from asymmetry of the periodic detachment of the boundary layer. The Reynolds number was 3·10³–10⁴.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 162–164, 1973.The authors wish to thank V. P. Borovikov for his assistance in organizing the experiments.     

Empirical foundation and axiomatic treatment of non-equilibrium temperature

Summary On the basis of well known empirems of classical thermodynamics, such as the First and Zero^th Laws, which lead to the definition of calorimeter systems by which heat exchanges can be measured, thermal interaction between thermally homogeneous systems is investigated by methods of set theory. In connexion with Carnap's axiom for a classical measuring quantity a thermodynamic analogue of the thermostatic temperature can be developed by generalized empirems which govern the thermal interaction between non-equilibrium and thermally homogeneous systems. An empirical identification of the contact temperature and its field formulation are given.I thank Assistant Prof. G. Brunk for stimulating discussions. This paper was prepared in unit FPS 9/1 at the Technische Universität Berlin.     

Calculation of friction and heat and mass exchange on rough permeable plane and axisymmetric bodies

The most effective methods of thermal shielding are characterized by the presence of a normal component of the velocity on the wall. They include porous cooling and the use of ablated coverings. If the heat-shielding materials have a granulated microstructure, their thermal expansion leads to roughness of the surface, as in the case of porosity of the wall. The present paper presents an integral method for calculating the drag and heat and mass transfer to a rough permeable surface in the case of a gradient flow of a compressible reacting gas.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 37–46, September–October, 1979.It is a pleasure to thank J. A. Schetz, who kindly sent tables of his experimental data, and also E. G. Zaulichny for discussing the work.     

Generalized characteristics in hyperbolic systems of conservation laws

In Memoriam Ronald J. DiPerna     

Stability of solutions of the Navier-Stokes equations backward in time

Communicated by J. Serrin     

Fit regions and functions of bounded variation

Dedicated to James B. Serrin on the occasion of his sixtieth birthday     

Influence of disturbances generated by the nozzle boundary layer on the heat exchange on the cylindrical nose of a body in a hypersonic flow

The heat transfer to a cylindrical surface whose generators are perpendicular to the freestream direction is investigated. Experiments were carried out in a short-duration wind tunnel at Mach numbers M=6 and 16. At M=6, the Reynolds number based on the cylinder diameter was varied on the range from 2.2·10⁴ to 0.95·10⁶ for the purpose of studying the effect of acoustic disturbances generated by the nozzle boundary layer on the heat exchange. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 125–131, January–February, 1999. The study was financially supported by ONERA (France). The authors wish to thank V. N. Gusev, S. M. Boldyrev, S. N. Krutii, and R. A. Kazanskii from TsAGI and J. Délery and B. Chanetz from ONERA for their assistance with the investigation.     

Existenzbeweis für cnoidal waves unter berücksichtigung der oberflächenspannung

Ohne ZusammenfassungHerrn Prof. Herbert Beckert zum 50. Geburtstag Vorgelegt von J. Serrin     

Memory effects and homogenization

Dedicated to Bernard D. Coleman on his sixtieth birthday     

Global Hopf bifurcation of two-parameter flows

The behavior of center-indices, as introduced by J. Mallet-Paret & J. Yorke, is analyzed for two-parameter flows. The integer sum of center-indices along a one-dimensional curve in parameter space is called the H-index. A nonzero H-index implies global Hopf bifurcation. The index H is not a homotopy invariant. This fact is due to the occurrence of stationary points with an algebraically double eigenvalue zero, which we call B-points. To each B-point we assign an integer B-index, such that the H-index relates to the B-indices by a formula such as occurs in the calculus of residues.This formula is easily applied to study global bifurcation of periodic solutions in diffusively coupled two-cells of chemical oscillators and to treat spatially heterogeneous time-periodic oscillations in porous catalysts.Dedicated to the memory of Charlie Conley     

Self-similar solutions for infiltration of dopant into semiconductors

Communicated by J. Serrin     

Nonexistence of positive solutions and oscillation criteria for second-order semilinear elliptic inequalities

Communicated by J. Serrin     

Monotone flows in N-dimensional partially saturated porous media: Lipschitz-continuity of the interface

Communicated by J. B. McLeod     

Instability of an equilibrium in a potential field

Communicated by P. J. Holmes     

Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations

Communicated by J. B. McLeod     

Uniform estimates for a variational problem with small parameters

Communicated by J. M. Ball     

Zur Existenz von Minimallösungen zweifach-unendlicher dreigliedriger linearer Rekursionen vom Poincará-Perronschen Typ

Ohne Zusammenfassung Vorgelegt von J. Meixner     

Auβenraumaufgaben zur plattengleichung

Ohne Zusammenfassung Vorgelegt von J. Meixner