Observability for the one-dimensional heat equation
Observability inequalities and measurable sets
This paper presents two observability inequalities for the heat equation over . In the first one, the observation is from a subset of positive measure in , while in the second, the observation is from a subset of positive surface measure on . It also proves the Lebeau-Robbiano spectral inequality when is a bounded Lipschitz and locally star-shaped domain. Some applications for the above-mentioned observability inequalities are provided.
On a boundary value problem for the heat equation
On a conjugate semi-variational method for parabolic equations
On a free boundary problem associated with combustion and solidification
On a generalized heat potential
On a heat potential
On a heat potential (Preliminary communication)
On a Parabolic Symmetry Problem.
On a phase transition model of Penrose-Fife type
We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.
On a plane heat-conductivity theory problem with mixed boundary conditions.
On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media
Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding...
On an initial inverse problem in nonlinear heat equation associated with time-dependent coefficient
In this paper, a nonlinear backward heat problem with time-dependent coefficient in the unbounded domain is investigated. A modified regularization method is established to solve it. New error estimates for the regularized solution are given under some assumptions on the exact solution.
On an integral inequality with a kernel singular in time and space.
On Borel summable solutions of the multidimensional heat equation
We give a new characterisation of Borel summability of formal power series solutions to the n-dimensional heat equation in terms of holomorphic properties of the integral means of the Cauchy data. We also derive the Borel sum for the summable formal solutions.
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation...
On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations∗∗∗
Local and global Carleman estimates play a central role in the study of some partial differential equations regarding questions such as unique continuation and controllability. We survey and prove such estimates in the case of elliptic and parabolic operators by means of semi-classical microlocal techniques. Optimality results for these estimates and some of their consequences are presented. We point out the connexion of these optimality results to the local phase-space geometry after conjugation...
On Continuous Dependence, on Noncharacteristic Cauchy Data, for Level Lines of Solutions of the Heat Equation.
On coupled thermoelastic vibration of geometrically nonlinear thin plates satisfying generalized mechanical and thermal conditions on the boundary and on the surface
The vibration problem in two variables is derived from the spatial situation (a plate as a three-dimensional body) on the basis of geometrically nonlinear plate theory (using Kármán's hypothesis) and coupled linear thermoelasticity. That leads to coupled strongly nonlinear two-dimensional equilibrium and heat conducting equations (under classical mechanical and thermal boundary conditions). For the generalized problem with subgradient conditions on the boundary and in the domain (including also...
On existence of harmonic maps from a surface to the spcae of it