On the Convergence of Finite-Difference Schemes for Parabolic Equations with Variable Coefficients.
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the convergence of the backward Euler algorithm for the multidimensional heat equation
The backward Euler algorithm for the multidimensional nonhomogeneous heat equation is analyzed, based on the finite element method. The existence and uniqueness of the numerical solution is investigated. Also, the convergence of the numerical solutions is studied.
On the cost of null-control of an artificial advection-diffusion problem
In this paper we study the null-controllability of an artificial advection-diffusion system in dimension n. Using a spectral method, we prove that the control cost goes to zero exponentially when the viscosity vanishes and the control time is large enough. On the other hand, we prove that the control cost tends to infinity exponentially when the viscosity vanishes and the control time is small enough.
On the derivation of the modified equation for the analysis of linear numerical methods
On the differential system governing flows in magnetic field with data in .
On the Dirichlet problem for fully nonlinear parabolic equations
On the discrete maximum principle for parabolic difference operators
On the discretization of a partial differential equation in the neighborhood of a periodic orbit.
On the discretization of degenerate sweeping processes.
On the dissipation layer of radial bearings.
On the distributional solution of the inverse problem induced by the heat kernel method.
On the domain dependence of solutions to the two-phase Stefan problem
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains converge to a solution of the same problem on a domain where is the limit of in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on .
On the dynamics of nonautonomous parabolic systems involving the Grushin operators.
On the eigenfunction expansion method for semilinear dissipative equations in bounded domains and the Kuramoto-Sivashinsky equation in a ball
Presented herein is a method of constructing solutions of semilinear dissipative evolution equations in bounded domains. For small initial data this approach permits one to represent the solution in the form of an eigenfunction expansion series and to calculate the higher-order long-time asymptotics. It is applied to the spatially 3D Kuramoto-Sivashinsky equation in the unit ball B in the linearly stable case. A global-in-time mild solution is constructed in the space , s < 2, and the uniqueness...
On the equation in planar domains
The blow-up of solutions for a parabolic equation with nonlocal exponential nonlinearity is studied.
On the existence of a fundamental solution for a parabolic differential equation with unbounded coefficients
On the existence of classical solutions for differential-functional IBVP.
On the existence of free vibrations for a beam equation when the period is an irrational multiple of the length
The author examined non-zero -periodic (in time) solutions for a semilinear beam equation under the condition that the period is an irrational multiple of the length. It is shown that for a.e. (in the sense of the Lebesgue measure on ) the solutions do exist provided the right-hand side of the equation is sublinear.
On the existence of positive solutions for periodic parabolic sublinear problems.