Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem

DOI10.2748/tmj/1178225520zbMath0845.34038OpenAlexW2064030695MaRDI QIDQ1902880

Zhenghua Lin, Junyu Wang, Wen-jie Gao

Publication date: 3 December 1995

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225520

zbMATH Keywords

upper and lower solutionssimilarity solutionsfluid mechanicstwo-point boundary value problemsdiffusion theoryRayleigh problem

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Nonlinear boundary value problems for ordinary differential equations (34B15) PDEs in connection with fluid mechanics (35Q35) Nonlocal and multipoint boundary value problems for ordinary differential equations (34B10)

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Cites Work

• Unnamed Item
• Unnamed Item
• A generalized diffusion equation: Radial symmetries and comparison theorems
• A homotopic deformation along \(p\) of a Leray-Schauder degree result and existence for \((| u'| ^{p-2}u')'+f(t,u)=0\), \(u(0)=u(T)=0\), \(p>1\)
• A method to obtain some similarity solutions to the generalized Newtonian fluid
• Steady-state turbulent flow with reaction
• Coincidence degree, and nonlinear differential equations
• An introduction to nonlinear boundary value problems
• On the propagation properties of a nonlinear degenerate parabolic equation
• Existence of solutions to boundary value problems for second order differential equations
• Upper and lower solutions and semilinear second order elliptic equations with non-linear boundary conditions
• Some qualitative properties of solutions of a generalised diffusion equation
• On the equation of turbulent filtration in one- dimensional porous media
• Some General Existence Principles and Results for $(\phi (y')) = qf(t,y,y'),0 < t < 1$
• A free boundary problem for a generalized diffusion equation
• Existence theorems for second order boundary value problems