scholarly journals A differential problem for heat equation with a boundary condition with memory

1997 ◽  
Vol 10 (1) ◽  
pp. 95-101 ◽  
Author(s):  
M. Ciarletta
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Differential Problem ◽  
With Memory

Dynamic behavior of a heat equation with memory

2009 ◽  
Vol 32 (10) ◽  
pp. 1287-1310 ◽  
Author(s):  
Jun-Min Wang ◽  
Bao-Zhu Guo ◽  
Meng-Yin Fu
Keyword(s):  
Heat Equation ◽  
Dynamic Behavior ◽  
Heat Equation With Memory ◽  
With Memory

scholarly journals Boundary value controllability and observability problems for the wave and heat equation

1988 ◽  
Vol 29 (4) ◽  
pp. 461-479
Author(s):  
K.-D. Werner
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Finite Energy ◽  
Duality Principle ◽  
Spherical Region ◽  
Initial States ◽  
The Fourier Transform ◽  
Controllability And Observability

AbstractIn this paper, we study controllability and observability problems for the wave and heat equation in a spherical region in Rn, where the control enters in the mixed boundary condition. In the main result, we show that all “finite energy” initial states (i.e. (ω0, ν0) ∈ H1(Ω) × L2 (Ω)) can be steered to zero at time T, using a control f ∈ L2 (∂Ω × [0, T]), provided T > 2. On this basis, we use the duality principle to investigate initial observability for the wave equation. Applying the Fourier transform technique, we obtain controllability and observability results for the 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.

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