Approximate controllability for linear degenerate parabolic problems with bilinear control
@article{Cannarsa2011ApproximateCF, title={Approximate controllability for linear degenerate parabolic problems with bilinear control}, author={Piermarco Cannarsa and Giuseppe Floridia}, journal={ArXiv}, year={2011}, volume={abs/1106.4232} }
27 Citations
Superexponential Stabilizability of Degenerate Parabolic Equations via Bilinear Control
- MathematicsSpringer Proceedings in Mathematics & Statistics
- 2020
The aim of this paper is to prove the superexponential stabilizability to the ground state solution of a degenerate parabolic equation of the form \begin{equation*}…
Superexponential stabilizability of evolution equations of parabolic type via bilinear control
- MathematicsJournal of Evolution Equations
- 2020
We study the stabilizability of a class of abstract parabolic equations of the form $$\begin{aligned} u'(t)+Au(t)+p(t)Bu(t)=0,\qquad t\ge 0 \end{aligned}$$ u ′ ( t ) + A u ( t ) + p ( t ) B u ( t ) =…
Superexponential stabilizability of evolution equations of parabolic type via bilinear control
- Materials ScienceJournal of Evolution Equations
- 2020
We study the stabilizability of a class of abstract parabolic equations of the form u′(t)+Au(t)+p(t)Bu(t)=0,t≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…
Bilinear control of a degenerate hyperbolic equation
- Mathematics
- 2021
We consider the linear degenerate wave equation, on the interval (0, 1) wtt − (x αwx)x = p(t)μ(x)w, with bilinear control p and Neumann boundary conditions. We study the controllability of this…
Global Non-negative Approximate Controllability of Parabolic Equations with Singular Potentials
- MathematicsTrends in Control Theory and Partial Differential Equations
- 2019
In this work, we consider the linear \(1-d\) heat equation with some singular potential (typically the so-called inverse square potential). We investigate the global approximate controllability via a…
Local null controllability for degenerate parabolic equations with nonlocal term
- MathematicsNonlinear Analysis: Real World Applications
- 2018
Multiplicative controllability for nonlinear degenerate parabolic equations between sign-changing states
- MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2020
In this paper we study the global approximate multiplicative controllability for nonlinear degenerate parabolic Cauchy problems. In particular, we consider a one-dimensional semilinear degenerate…
Approximate multiplicative controllability for degenerate parabolic problems with Robin boundary conditions
- Mathematics
- 2011
IIn this work we study the global approximate multiplicative controllability for a weakly degenerate parabolic Cauchy-Robin problem. The problem is weakly degenerate in the sense that the diffusion…
Multiplicative controllability for semilinear reaction-diffusion equations with finitely many changes of sign
- Mathematics
- 2015
NumHyp 2015 Numerical Methods for Hyperbolic Systems with Source Terms and Applications
- Mathematics
- 2015
Scalar conservation laws ut + f(x, u)x = 0 with x-discontinuous, piecewise smooth flux f are not well-posed unless specific admissibility criteria are imposed at the locations of disccontinuity of…
43 References
Carleman estimates for degenerate parabolic operators with applications to null controllability
- Mathematics
- 2006
Abstract.We prove an estimate of Carleman type for the one dimensional heat equation
$$ u_t - \left( {a\left( x \right)u_x } \right)_x + c\left( {t,x} \right)u = h\left( {t,x} \right),\quad \left(…
Carleman Estimates for a Class of Degenerate Parabolic Operators
- MathematicsSIAM J. Control. Optim.
- 2008
The proof is based on the choice of suitable weighted functions and Hardy-type inequalities and deduce null controllability results for the degenerate one-dimensional heat equation with the same boundary conditions as above.
Global controllability properties for the semilinear heat equation with superlinear term
- Mathematics
- 1999
We discuss several global approximate controllability properties for the semilinear heat equation with superlinear reaction-convection term, governed in a bounded domain by locally distributed…
Persistent regional null contrillability for a class of degenerate parabolic equations
- Mathematics
- 2004
Motivated by physical models and the so-called Crocco equation,
we study the controllability properties of
a class of degenerate parabolic equations.
Due to degeneracy, classical null…
Strongly continuous semigroups, weak solutions, and the variation of constants formula
- Mathematics
- 1977
Let A be a densely defined closed linear operator on a Banach space X, and let f E L'(O,r;X). A definition of weak solutions of the equation u = Au + f(t) is given. It is shown that a necessary and…
Global non-negative controllability of the semilinear parabolic equation governed by bilinear control
- Mathematics
- 2002
We study the global approximate controllability of the one dimensional semilinear convection-diusion-reaction equation governed in a bounded domain via the coecient (bilinear con- trol) in the…
Strongly Continuous Semigroups
- Mathematics
- 2012
In Chapter 2 we showed that the examples of Chapter 1, which were described by ordinary differential equations, can be written as a first-order differential equation
$$\dot{x}(t) = Ax(t) + Bu(t),…
Approximate multiplicative controllability for degenerate parabolic problems with Robin boundary conditions
- Mathematics
- 2011
IIn this work we study the global approximate multiplicative controllability for a weakly degenerate parabolic Cauchy-Robin problem. The problem is weakly degenerate in the sense that the diffusion…
Controllability of Partial Differential Equations Governed by Multiplicative Controls
- Mathematics
- 2010
Multiplicative Controllability of Parabolic Equations.- Global Nonnegative Controllability of the 1-D Semilinear Parabolic Equation.- Multiplicative Controllability of the Semilinear Parabolic…