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901
This paper is devoted to some nonlinear propagation phenomena in periodic and more
general domains, for reaction-diffusion equations with Kolmogorov–Petrovsky–Piskunov (KPP) type nonlinearities. The case of periodic domains with periodic underlying excitable media is a
follow-up of the article [7]. It is proved that the minimal speed of pulsating fronts is given by a variational formula involving linear eigenvalue problems. Some consequences concerning the influence of the geometry of the domain,...
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell 14 (1998) 826–835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.
We study a time-delay regularization of the anisotropic
diffusion model for image denoising
of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell12 (1990) 629–639], which has been proposed by Nitzberg and Shiota [IEEE Trans. Pattern Anal. Mach. Intell14 (1998) 826–835].
In the two-dimensional case, we show the convergence of a numerical
approximation and the existence of a weak solution. Finally, we show some
experiments on images.
A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
We study boundary value problems for quasilinear parabolic equations when the initial condition is replaced by periodicity in the time variable. Our approach is to relate the theory of such problems to the classical theory for initial-boundary value problems. In the process, we generalize many previously known results.
We consider a Vlasov-Fokker-Planck equation governing the evolution
of the density of interacting and diffusive matter in the space of
positions and velocities.
We use a probabilistic interpretation to obtain convergence towards
equilibrium in Wasserstein distance with an explicit exponential
rate. We also prove a propagation of chaos property for an
associated particle system, and give rates on the approximation of
the solution by the particle system. Finally, a transportation
inequality...
It is known that the nonlinear nonhomogeneous backward Cauchy problem , with , where is a densely defined positive self-adjoint unbounded operator on a Hilbert space, is ill-posed in the sense that small perturbations in the final value can lead to large deviations in the solution. We show, under suitable conditions on and , that a solution of the above problem satisfies an integral equation involving the spectral representation of , which is also ill-posed. Spectral truncation is used...
We provide two examples of a regular curve evolving by curvature with a forcing term, which degenerates in a set having an interior part after a finite time.
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