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.
Observations on Blow Up and Dead Cores for Nonlinear Parabolic Equations.
On a blow-up estimate for a higher order semilinear parabolic equation
On a boundary value problem for an equation of the type of non-stationary filtration
On a boundary value problem for the heat equation
On a Caginalp phase-field system with a logarithmic nonlinearity
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
On a Cahn–Hilliard model for phase separation with elastic misfit
On a class of nonlinear degenerate parabolic equations
On a class of nonlinear reaction-diffusion systems with nonlocal boundary conditions.
On a class of parabolic integro-differential equations.
On a Class of Retarded Partial Differential Equations.
On a Class of Time Inhomogeneous Nonsingular Flows and Schrödinger Operators.
On a Class of Unilateral Evolution Problems.
On a complete initial-boundary value problem for parabolic pseudo-differential operators.
On a conjugate semi-variational method for parabolic equations
On a conjugate semi-variational method for parabolic equations
On a conserved Penrose-Fife type system
We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.
On a critical threshold for nonlinear diffusion equations.
We study some aspects of the asymptotic behavior of the solutions to a class of nonlinear parabolic equations.
On a Decay Property of Weak Solution for Semilinear Evolution Equation of Parabolic Type and Its Applications.