A new perturbation criterion for two nonlinear m-accretive operators with applications to semilinear equations.
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A new proof of Kellerer’s theorem
In this paper, we present a new proof of the celebrated theorem of Kellerer, stating that every integrable process, which increases in the convex order, has the same one-dimensional marginals as a martingale. Our proof proceeds by approximations, and calls upon martingales constructed as solutions of stochastic differential equations. It relies on a uniqueness result, due to Pierre, for a Fokker-Planck equation.
A new version of the fast Gauss transform.
A non-convex diffusion model for simultaneous image denoising and edge enhancement.
A nonhomogeneous backward heat problem: regularization and error estimates.
A nonlinear degenerate parabolic equation
A nonlinear diffusion equation with nonlinear boundary conditions: Method of lines
A nonlinear evolution equation modelling the Marangoni effect : existence of solution and numerical methods
A nonlinear heat equation with temperature-dependent parameters.
A nonlinear oblique derivative boundary value problem for the heat equation. Part 1 : basic results
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...
A nonlocal coagulation-fragmentation model
A new nonlocal discrete model of cluster coagulation and fragmentation is proposed. In the model the spatial structure of the processes is taken into account: the clusters may coalesce at a distance between their centers and may diffuse in the physical space Ω. The model is expressed in terms of an infinite system of integro-differential bilinear equations. We prove that some results known in the spatially homogeneous case can be extended to the nonlocal model. In contrast to the corresponding local...
A note of uniqueness on the Cauchy problem for Schrödinger or heat equations with degenerate elliptic principal parts
We study the local uniqueness in the Cauchy problem for Schrödinger or heat equations whose principal parts are nonnegative. We show the compact uniqueness under a weak form of pseudo convexity. This makes up for the known results under the conormal pseudo convexity given by Tataru, Hörmander, Robbiano- Zuily and L. T'Joen. Our method is based on a kind of integral transform and a weak form of Carleman estimate for degenerate elliptic operators.
A note on a heat potential and the parabolic variation
A note on asymptotic expansion for a periodic boundary condition
The aim of this contribution is to present a new result concerning asymptotic expansion of solutions of the heat equation with periodic Dirichlet–Neuman boundary conditions with the period going to zero in D.
A note on Chebyshev series solution of the Crank-Gupta equation.
A note on nonhomogeneous initial and boundary conditions in parabolic problems solved by the Rothe method
When solving parabolic problems by the so-called Rothe method (see K. Rektorys, Czech. Math. J. 21 (96), 1971, 318-330 and other authors), some difficulties of theoretical nature are encountered in the case of nonhomogeneous initial and boundary conditions. As a rule, these difficulties lead to rather unnatural additional conditions imposed on the corresponding bilinear form and the initial and boundary functions. In the present paper, it is shown how to remove such additional assumptions in the...