scholarly journals Null controllability for a heat equation with dynamic boundary conditions and drift terms

2020 ◽  
Vol 9 (2) ◽  
pp. 535-559
Author(s):  
Abdelaziz Khoutaibi ◽  
◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Null Controllability ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Drift Terms

scholarly journals Stackelberg-Nash null controllability of heat equation with general dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Idriss Boutaayamou ◽  
Lahcen Maniar ◽  
Omar Oukdach
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Hierarchical Control ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Drift Terms ◽  
Controllability Result ◽  
General Dynamic

<p style='text-indent:20px;'>This paper deals with the hierarchical control of the anisotropic heat equation with dynamic boundary conditions and drift terms. We use the Stackelberg-Nash strategy with one leader and two followers. To each fixed leader, we find a Nash equilibrium corresponding to a bi-objective optimal control problem for the followers. Then, by some new Carleman estimates, we prove a null controllability result.</p>

scholarly journals On a singular heat equation with dynamic boundary conditions

2016 ◽  
Vol 97 (1-2) ◽  
pp. 27-59 ◽  
Author(s):  
Giulio Schimperna ◽  
Antonio Segatti ◽  
Sergey Zelik
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals Null controllability for parabolic equations with dynamic boundary conditions

2017 ◽  
Vol 6 (3) ◽  
pp. 381-407 ◽  
Author(s):  
Lahcen Maniar ◽  
◽  
Martin Meyries ◽  
Roland Schnaubelt ◽  
◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Parabolic Equations ◽  
Null Controllability ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals Identification of source terms in heat equation with dynamic boundary conditions

2021 ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah‐Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Source Terms ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

scholarly journals Linear evolution equations on the half-line with dynamic boundary conditions

2021 ◽  
pp. 1-33
Author(s):  
D. A. SMITH ◽  
W. Y. TOH
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Evolution Equations ◽  
Half Line ◽  
Robin Problem ◽  
Dynamic Boundary Conditions ◽  
Transform Method ◽  
Linear Evolution ◽  
Robin Condition ◽  
Linear Evolution Equations

The classical half-line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $$bq(0,t) + {q_x}(0,t) = 0$$ is replaced with a dynamic Robin condition; $$b = b(t)$$ is allowed to vary in time. Applications include convective heating by a corrosive liquid. We present a solution representation and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half-line, with arbitrary linear dynamic boundary conditions.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions

2006 ◽  
Vol 279 (13-14) ◽  
pp. 1448-1462 ◽  
Author(s):  
Ralph Chill ◽  
Eva Fašangová ◽  
Jan Prüss
Keyword(s):  
Boundary Conditions ◽  
Steady States ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary ◽  
Convergence To Steady States
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