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Observability inequalities and measurable sets

Jone Apraiz, Luis Escauriaza, Gengsheng Wang, C. Zhang (2014)

Journal of the European Mathematical Society

This paper presents two observability inequalities for the heat equation over $Ω \times (0, T)$ . In the first one, the observation is from a subset of positive measure in $Ω \times (0, T)$ , while in the second, the observation is from a subset of positive surface measure on $\partial Ω \times (0, T)$ . It also proves the Lebeau-Robbiano spectral inequality when $Ω$ is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.

On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations [Book]

W. M. Zajączkowski (1990)

On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

Ira Neitzel, Fredi Tröltzsch (2008)

Control and Cybernetics

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Displaying 1 – 20 of 50

Observability inequalities and measurable sets

Observations on Blow Up and Dead Cores for Nonlinear Parabolic Equations.

On a boundary value problem for an equation of the type of non-stationary filtration

On a complete initial-boundary value problem for parabolic pseudo-differential operators.

On a conjugate semi-variational method for parabolic equations

On an initial-boundary value problem for the equation $w_{t} = w_{x x} - x w_{y}$

On an initial-boundary value problem for the parabolic system which appears in free boundary problems for compressible Navier-Stokes equations [Book]

On behaviour of non-negative weak solutions of parabolic equations at the boundary

On classical solutions of mixed boundary problems for one-dimensional parabolic equation of second order.

On comparison principles for parabolic equations with nonlocal boundary conditions.

On convergence of regularization methods for nonlinear parabolic optimal control problems with control and state constraints

On exact solutions of one-dimensional diffusion problems with free boundaries for parabolic equations.

On explicit and numerical solvability of parabolic initial-boundary value problems.

On initial boundary value problems with equivalued surface for nonlinear parabolic equations.

On internal approximations of parabolic problems

On $L^{p}$ -estimates for solutions of the Cauchy problem for parabolic differential equations

On nonlocal problems for ordinary differential equations and on a nonlocal parabolic transmission problem.

On Numerical Asymptotic Behavior of Finite Element Solutions for Parabolic Equations.

On parabolic initial-boundary value problems with critical growth for the gradient

On positive solutions of some periodic parabolic eigenvalue problem with a weight function

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