Mixed problem with an integral space variable condition for a Third order parabolic equation of mixed type

2010 ◽  
Author(s):  
Ali Hameida
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Mixed Type ◽  
Space Variable ◽  
Third Order ◽  
Order Parabolic Equation ◽  
Equation Of Mixed Type ◽  
Variable Condition

scholarly journals Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type

2001 ◽  
Vol 26 (7) ◽  
pp. 417-426 ◽  
Author(s):  
M. Denche ◽  
A. L. Marhoune
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Mixed Problem ◽  
Mixed Type ◽  
Order Partial Differential Equation ◽  
Third Order ◽  
Partial Differential ◽  
Integral Boundary ◽  
Equation Of Mixed Type

We study a mixed problem with integral boundary conditions for a third-order partial differential equation of mixed type. We prove the existence and uniqueness of the solution. The proof is based on two-sided a priori estimates and on the density of the range of the operator generated by the considered problem.

scholarly journals On a third order parabolic equation with a nonlocal boundary condition

2000 ◽  
Vol 13 (2) ◽  
pp. 181-195 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Nonlocal Boundary Condition ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Third Order ◽  
Order Parabolic Equation ◽  
Classical Boundary ◽  
Total Mass Flux

In this paper we demonstrate the existence, uniqueness and continuous dependence of a strong solution upon the data, for a mixed problem which combine classical boundary conditions and an integral condition, such as the total mass, flux or energy, for a third order parabolic equation. We present a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the studied problem.

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