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Start Over Coverage 175-184

3. Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p-Laplacian

Creator:
Naito, Yūki
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
boundary value problem, half-linear differential equation, Sturm comparison theorem, and half-linear Prüfer transformation
Language:
English
Description:
We consider the boundary value problem involving the one dimensional pLaplacian, and establish the precise intervals of the parameter for the existence and nonexistence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Steady laminar Couette flow of a dilatant fluid along a channel with suction at a bounding wall

Creator:
Sacheti, N.C., Chandran, P., Jaju, R.P., and Bhatt, B.S.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
non-Newtonian fluid, plane Couette flow, similarity transformation, suction, skin friction, Nenewtonská tekutina, rovinné prúdenie Couette, transformácia podobnosti, sanie, and povrchové trenie
Language:
Slovak
Description:
We consider a special dilatant fluid model for which the apparent viscosity can be expressed as a polynomial in the second scalar invariant of the rate of strain tensor. The model has been used to investigate the steady plane Couette flow of a non-Newtonian fluid through a channel with suction, assumed small, at the lower porous wall. The introduction of a similarity transformation in the perturbed governing partial differential equations of the flow leads to a system of coupled non-linear ordinary differential equations. The solutions of these equations have been obtained analytically as a power series in the suction parameter . The combined effects of the non-Newtonian and the suction parameters on the longitudinal and transverse velocity profiles as well as the skin friction, have been discussed. The validity of the analytical solutions has also been checked with the corresponding numerical solutions for small values of the governing parameters. and Štúdia sa zaoberá sa špeciálnym modelom nenewtonskej tekutiny, pre ktorú sa môže skutočná viskozita vyjadriť vo forme polynomickej závislosti na druhom skalárnom invariante tenzora rýchlosti deformácie. Model bol využitý na štúdium ustáleného Couetteho rovinného prúdenia nenewtonskej tekutiny v kanáli so saním cez porézne steny. Zavedenie transformácie podobnosti do lineanizovaných parciálnych diferenciálnych rovníc vedie k systému obyčajných nelineárnych diferenciálnych rovníc. Ich riešenie sme získali vo forme potenčného radu od sacieho parametra λ. Analyzovali sme vplyv rozťažnosti tekutiny a sacieho parametra na pozdĺžny a priečny rýchlostny profil, ako aj na povrchové trenie. Platnosť analytického riešenia sme porovnali s numerickým riešením pre malé hodnoty použitých parametrov.
Rights:
http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public