Total Variation Flow and Sign Fast Diffusion in one dimension
نویسندگان
چکیده
We consider the dynamics of the Total Variation Flow (TVF) ut = div(Du/|Du|) and of the Sign Fast Diffusion Equation (SFDE) ut = ∆ sign(u) in one spatial dimension. We find the explicit dynamic and sharp asymptotic behaviour for the TVF, and we deduce the one for the SFDE by an explicit correspondence between the two equations.
منابع مشابه
Mathematical Modeling of Gas Separation Process with Flat Carbon Membrane
Carbon molecular sieve membranes (CMSMs) have been considered as very promising candidates for gas separation, in terms of separation properties as well as thermal and chemical stability. Due to the numerous advantages and wide applications of carbon membranes, their application for gas separation is of special importance. Because of the importance of carbon membranes and a large number of stud...
متن کاملVariation in chemical components and biological activity of Pterocarya fraxinifolia Lam. stems at different developmental stages
Background and objectives: Pterocarya fraxinifolia Lam. is a deciduous, fast-growing tree from walnut family. The stem barks and fruits of the plant have been used as diaphoretic in traditional medicine. Variation in the quantity and quality of the essential oil and extract of stems of the plant at different developmental stages was evaluated in addition to assessing t...
متن کاملAnisotropic Total Variation Flow of Non-divergence Type on a Higher Dimensional Torus
We extend the theory of viscosity solutions to a class of very singular nonlinear parabolic problems of non-divergence form in a periodic domain of an arbitrary dimension with diffusion given by an anisotropic total variation energy. We give a proof of a comparison principle, an outline of a proof of the stability under approximation by regularized parabolic problems, and an existence theorem f...
متن کاملDynamic Response Analysis of the Planar and Tubular Solid Oxide Fuel Cells to the Inlet Air Mass Flow Rate Variation
The purpose of present study is to investigate the dynamic response of two conventional types of solid oxide fuel cells to the inlet air mass flow rate variation. A dynamic compartmental model based on CFD principles is developed for two typical planar and tubular SOFC designs. The model accounts for transport processes (heat and mass transfer), diffusion processes, electrochemical processes, a...
متن کاملDiffusion Process for Multi - Repairmen Machining System with Spares Aand Balking
In this paper we describe G/G/R+s multi- repairmen machining system with balking. The system consists of M operating machines, S spare machines, R permanent and s additional repairmen. Assuming the discrete flow of machines by continuous one, the diffusion approximation technique for the machine repair system has developed. The system will be in normal working mode if there is M operating machi...
متن کامل