scholarly journals Null controllability for a coupled system of degenerate/singular parabolic equations in nondivergence form

2018 ◽  
pp. 1-28
Author(s):  
Jawad Salhi
Keyword(s):  
Parabolic Equations ◽  
Coupled System ◽  
Null Controllability ◽  
Nondivergence Form ◽  
Singular Parabolic Equations

scholarly journals Carleman estimates and null controllability of a class of singular parabolic equations

2018 ◽  
Vol 8 (1) ◽  
pp. 1057-1082
Author(s):  
Runmei Du ◽  
Jürgen Eichhorn ◽  
Qiang Liu ◽  
Chunpeng Wang
Keyword(s):  
Control Systems ◽  
Parabolic Equations ◽  
Null Controllability ◽  
Carleman Estimates ◽  
Energy Estimates ◽  
Semilinear Parabolic Equations ◽  
Linearized Equations ◽  
Singular Parabolic Equations ◽  
Semilinear Parabolic

Abstract In this paper, we consider control systems governed by a class of semilinear parabolic equations, which are singular at the boundary and possess singular convection and reaction terms. The systems are shown to be null controllable by establishing Carleman estimates, observability inequalities and energy estimates for solutions to linearized equations.

scholarly journals Null controllability for a class of stochastic singular parabolic equations with the convection term

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Lin Yan ◽  
Bin Wu
Keyword(s):  
Parabolic Equations ◽  
Dimensional Space ◽  
Adjoint System ◽  
Null Controllability ◽  
Observability Inequality ◽  
Convection Term ◽  
One Dimensional ◽  
Singular Parabolic Equation ◽  
Approximate System ◽  
Singular Parabolic Equations

<p style='text-indent:20px;'>This paper concerns the null controllability for a class of stochastic singular parabolic equations with the convection term in one dimensional space. Due to the singularity, we first transfer to study an approximate nonsingular system. Next we establish a new Carleman estimate for the backward stochastic singular parabolic equation with convection term and then an observability inequality for the adjoint system of the approximate system. Based on this observability inequality and an approximate argument, we obtain the null controllability result.</p>

scholarly journals Boundary controllability for a coupled system of degenerate/singular parabolic equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Brahim Allal ◽  
Abdelkarim Hajjaj ◽  
Jawad Salhi ◽  
Amine Sbai
Keyword(s):  
Spectral Analysis ◽  
Parabolic Equations ◽  
Moment Method ◽  
Coupled System ◽  
Control Cost ◽  
Boundary Controllability ◽  
The Moment ◽  
Singular Parabolic Equations

<p style='text-indent:20px;'>In this paper we study the boundary controllability for a system of two coupled degenerate/singular parabolic equations with a control acting on only one equation. We analyze both approximate and null boundary controllability properties. Besides, we provide an estimate on the null-control cost. The proofs are based on a detailed spectral analysis and the use of the moment method by Fattorini and Russell together with some results on biorthogonal families.</p>

scholarly journals A Boundary Estimate for Singular Sub-Critical Parabolic Equations

2020 ◽  
Author(s):  
Ugo Gianazza ◽  
Naian Liao
Keyword(s):  
Modulus Of Continuity ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Boundary Point ◽  
Cylindrical Domain ◽  
Boundary Estimate ◽  
Critical Range ◽  
Type Integral ◽  
Wiener Type ◽  
Singular Parabolic Equations

Abstract We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

scholarly journals An Inverse Source Problem for Singular Parabolic Equations with Interior Degeneracy

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Khalid Atifi ◽  
Idriss Boutaayamou ◽  
Hamed Ould Sidi ◽  
Jawad Salhi
Keyword(s):  
Numerical Solution ◽  
Parabolic Equations ◽  
Measurement Data ◽  
Gradient Methods ◽  
Stability Estimate ◽  
Inverse Source Problem ◽  
Output Least Squares ◽  
Singular Parabolic Equations ◽  
Interior Degeneracy ◽  
Least Squares Approach

The main purpose of this work is to study an inverse source problem for degenerate/singular parabolic equations with degeneracy and singularity occurring in the interior of the spatial domain. Using Carleman estimates, we prove a Lipschitz stability estimate for the source term provided that additional measurement data are given on a suitable interior subdomain. For the numerical solution, the reconstruction is formulated as a minimization problem using the output least squares approach with the Tikhonov regularization. The Fréchet differentiability of the Tikhonov functional and the Lipschitz continuity of the Fréchet gradient are proved. These properties allow us to apply gradient methods for numerical solution of the considered inverse source problem.

Nonlinear Singular Parabolic Equations

2020 ◽  
pp. 21-36
Author(s):  
Piotr Biler ◽  
Tadeusz Nadzieja ◽  
Andrzej Raczyński
Keyword(s):  
Parabolic Equations ◽  
Singular Parabolic Equations
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