Null boundary controllability of a one-dimensional heat equation with an internal point mass and variable coefficients

Null Controllability of a Nonlinear Heat Equation

Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients

We derive global Carleman estimates for one-dimensional linear parabolic operators ∂t ± ∂x(c∂x) with a coefficient c with bounded variations. These estimates are obtained by approximating c by piecewise regular coefficients, cε, and passing to the limit in the Carleman estimates associated to the operators defined with cε. Such estimates yield results of controllability to the trajectories for ...

Finite Dimensional Null Controllability for the Semilinear Heat Equation

ABSTRACI’. We study a finite dimensional version of the null controllability problem for semilinear heat equations in bounded domains R of R” with Dirichlet boundary conditions. The control acts on any open an non-empty subset of R. The question under consideration is the following: given an initial state, a control time t = 2’ and a finite dimensional subspace E of L”(n), is there a control su...

An analytic solution for a non-local initial-boundary value problem including a partial differential equation with variable coefficients

‎This paper considers a non-local initial-boundary value problem containing a first order partial differential equation with variable coefficients‎. ‎At first‎, ‎the non-self-adjoint spectral problem is derived‎. ‎Then its adjoint problem is calculated‎. ‎After that‎, ‎for the adjoint problem the associated eigenvalues and the subsequent eigenfunctions are determined‎. ‎Finally the convergence ...

Transient Three-Dimensional Thermal Analysis of a Slab with internal heat generation and heated by a Point Moving Heat Source

In this work, analysis of transient three-dimensional heat transfer in a slab with internal heat generation and heated by a point moving heat source along its axis is carried out using integral transforms methods. The heat input into slab or workpiece by the moving heat source is considered in the model. From the results, it was established that the temperature of the material during the heat t...