scholarly journals Linear parabolic equations with venttsel initial boundary conditions

1994 ◽  
Vol 50 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Yi Zeng ◽  
Yousong Luo
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Initial Boundary ◽  
Engineering Problem ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Boundary Condition ◽  
Linear Parabolic Equations

The Schauder estimates for solutions of linear second order parabolic equations with Venttsel initial boundary conditions are proved, and existence and uniqueness of classical solutions under such an initial boundary condition are established. An application to an engineering problem is also given.

NEW MODELS IN MICROPOLAR FLUID AND THEIR APPLICATION TO LUBRICATION

2005 ◽  
Vol 15 (03) ◽  
pp. 343-374 ◽  
Author(s):  
GUY BAYADA ◽  
NADIA BENHABOUCHA ◽  
MICHÈLE CHAMBAT
Keyword(s):  
Boundary Condition ◽  
Friction Coefficient ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Micropolar Fluid ◽  
Reynolds Equation ◽  
Slip Boundary Condition ◽  
Slip Boundary ◽  
New Models ◽  
Uniqueness Of The Solution

A thin micropolar fluid with new boundary conditions at the fluid-solid interface, linking the velocity and the microrotation by introducing a so-called "boundary viscosity" is presented. The existence and uniqueness of the solution is proved and, by way of asymptotic analysis, a generalized micropolar Reynolds equation is derived. Numerical results show the influence of the new boundary conditions for the load and the friction coefficient. Comparisons are made with other works retaining a no slip boundary condition.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals The periodic quasigeostrophic equations: existence and uniqueness of strong solutions

1982 ◽  
Vol 91 (3-4) ◽  
pp. 185-203 ◽  
Author(s):  
A. F. Bennett ◽  
P. E. Kloeden
Keyword(s):  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Coupled System ◽  
Classical Solutions ◽  
Schauder Estimates ◽  
Initial Vorticity ◽  
Relative Potential ◽  
Quasigeostrophic Equations

SynopsisThe periodic quasigeostrophic equations are a coupled system of a second order elliptic equation for a streamfunction and first order hyperbolic equations for the relative potential vorticity and surface potential temperatures, on a three-dimensional domain which is periodic in both horizontal spatial co-ordinates. Such equations are used in both numerical and theoretical studies in meteorology and oceanography. In this paper Schauder estimates and a Schauder fixed point theorem are used to prove the existence and uniqueness of strong, that is classical, solutions of the periodic quasigeostrophic equations for a finite interval of time, which is inversely proportional to the sum of the norms of the initial vorticity and surface temperatures.

scholarly journals TWO INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR ONE-DIMENSION HYPERBOLIC EQUATION

2017 ◽  
Vol 17 (2) ◽  
pp. 46-56
Author(s):  
L.S. Pulkina ◽  
M.V. Strigun
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
One Dimension ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

In this paper, the initial-boundary value problems for hyperbolic equationwith nonlinear boundary conditions are considered. Existence and uniqueness ofgeneralized solution are proved.

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