On a time-discretization method for a semilinear heat equation with purely integral conditions in a nonclassical function space

2007 ◽  
Vol 66 (3) ◽  
pp. 604-623 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Heat Equation ◽  
Function Space ◽  
Time Discretization ◽  
Discretization Method ◽  
Integral Conditions ◽  
Semilinear Heat Equation

scholarly journals Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Time Discretization ◽  
Neumann Condition ◽  
Integral Boundary ◽  
Semilinear Heat Equation ◽  
Rothe Method ◽  
The Given

This paper is devoted to prove, in a nonclassical function space, the weak solvability of a mixed problem which combines a Neumann condition and an integral boundary condition for the semilinear one-dimensional heat equation. The investigation is made by means of approximation by the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable.

scholarly journals Rothe time-discretization method for a nonlocal problem arising in thermoelasticity

2005 ◽  
Vol 2005 (1) ◽  
pp. 13-28 ◽  
Author(s):  
Nabil Merazga ◽  
Abdelfatah Bouziani
Keyword(s):  
Continuous Dependence ◽  
Nonlocal Problem ◽  
Time Discretization ◽  
Boundary Integral ◽  
Time Variable ◽  
Discretization Method ◽  
Integral Conditions ◽  
Rothe Method ◽  
Semidiscrete Approximation ◽  
The Given

We investigate a model parabolic mixed problem with purely boundary integral conditions arising in the context of thermoelasticity. Using the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable, the questions of existence, uniqueness, and continuous dependence upon data of a weak solution are proved. Moreover, we establish convergence and derive an error estimate for a semidiscrete approximation.

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