Numerical blow-up time for a semilinear parabolic equation with nonlinear boundary conditions.
Numerical identification of a coefficient in a parabolic quasilinear equation
In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...
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 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
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 -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.