# An elementary proof of the lack of null controllability for the heat equation on the half line

@article{Kalimeris2020AnEP,
title={An elementary proof of the lack of null controllability for the heat equation on the half line},
author={Konstantinos Kalimeris and T{\"u}rker {\"O}zsari},
journal={Appl. Math. Lett.},
year={2020},
volume={104},
pages={106241}
}
• Published 2020
• Computer Science, Mathematics
• Appl. Math. Lett.
In this note, we give an elementary proof of the lack of null controllability for the heat equation on the half line by employing the machinery inherited by the unified transform, known also as the Fokas method. This approach also extends in a uniform way to higher dimensions and different initial-boundary value problems governed by the heat equation, suggesting a novel methodology for studying problems related to controllability.
5 Citations

#### Figures from this paper

Numerical computation of Neumann controllers for the heat equation on a finite interval
• Computer Science, Mathematics
• ArXiv
• 2021
A new numerical method which approximates Neumann type null controllers for the heat equation and is based on the Fokas method, which allows the realisation of an efficient numerical algorithm that requires small computational effort for determining the null controller with exponentially small error. Expand
The Modified Helmholtz Equation on a Regular Hexagon - The Symmetric Dirichlet Problem
• Computer Science, Mathematics
• Axioms
• 2020
If the modified Helmholtz equation in the regular hexagon with symmetric Dirichlet boundary conditions is odd, then this problem can be solved in closed form. Expand
The nonlinear Schrödinger equation on the half-line with a Robin boundary condition
• Mathematics
• Analysis and Mathematical Physics
• 2021
The initial-boundary value problem for the nonlinear Schrodinger equation on the half-line with initial data in Sobolev spaces $$H^s(0, \infty )$$ , $$1/2< s\leqslant 5/2$$ , $$s\ne 3/2$$ , andExpand
Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay
• Guenbo Hwang
• Mathematics
• Zeitschrift für Naturforschung A
• 2020
Abstract Initial-boundary value problems for the one-dimensional linear advection–dispersion equation with decay (LAD) are studied by utilizing a unified method, known as the Fokas method. The methodExpand
The linearized classical Boussinesq system on the half‐line
• Mathematics, Physics
• 2020
The linearization of the classical Boussinesq system is solved explicitly in the case of nonzero boundary conditions on the half-line. The analysis relies on the unified transform method of Fokas andExpand

#### References

SHOWING 1-9 OF 9 REFERENCES
On the lack of null-controllability of the heat equation on the half-line
• Mathematics
• 2000
We consider the linear heat equation on the half-line with a Dirichlet boundary control. We analyze the null-controllability problem. More precisely, we study the class of initial data that may beExpand
Exact Boundary Controllability for the Linear Korteweg--de Vries Equation on the Half-Line
• L. Rosier
• Mathematics, Computer Science
• SIAM J. Control. Optim.
• 2000
It is shown that the {\em exact} boundary controllability holds true in L^2 (0,+\infty )$provided that the solutions are not required to be in$L^{\infty }(0,T,L^2( 0,+ \infty ))\$. Expand
The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line
• Mathematics
• 2018
We study the local and global wellposedness of the initial-boundary value problem for the biharmonic Schrodinger equation on the half-line with inhomogeneous Dirichlet-Neumann boundary data. First,Expand
The Korteweg-de Vries equation on an interval
• Mathematics
• Journal of Mathematical Physics
• 2019
The initial-boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation on an interval is studied by extending a novel approach recently developed for the well-posedness of the KdV on theExpand
The nonlinear Schrödinger equation on the half-line
• Mathematics
• 2016
The initial-boundary value problem (ibvp) for the cubic nonlinear Schrödinger (NLS) equation on the half-line with data in Sobolev spaces is analysed via the formula obtained through the unifiedExpand
A Unified Approach To Boundary Value Problems
This book presents a new approach to analyzing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, a method that the author first introduced inExpand
A unified transform method for solving linear and certain nonlinear PDEs
• A. S. Fokas
• Mathematics
• Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
• 1997
A new transform method for solving initial boundary value problems for linear and for integrable nonlinear PDEs in two independent variables is introduced. This unified method is based on the factExpand
A new transform method for evolution partial differential equations
We introduce a new transform method for solving initial-boundary-value problems for linear evolution partial differential equations with spatial derivatives of arbitrary order. This method isExpand
Functional Analysis
A vector space over a field K (R or C) is a set X with operations vector addition and scalar multiplication satisfy properties in section 3.1. [1] An inner product space is a vector space X withExpand