The paper proves estimates for the partial derivatives of the solution to a time-fractional diffusion equation, posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is less regular than in the well-known case of classical diffusion.

In this paper we investigate a nonlocal reaction diffusion equation with potential, under Neumann boundary. We obtain the complete classification of the parameters for which the solution blows up in finite time or exists globally. Moreover, we study the blowup rate and the blowup set for the blowup solution. Key–Words: Nonlocal diffusion, Blow up, Blowup rate, Blowup set

Consider a nonlinear diffusion equation related to the p-Laplacian. Different from the usual evolutionary p-Laplacian equation, the equation is degenerate on the boundary due to the fact that the diffusion coefficient is dependent on the distance function. Not only the existence of the weak solution is established, but also the uniqueness of the weak solution is proved.

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

Besides common implant techniques, dopant diffusion enables steep diffusion profiles in heavily doped deep-source drain and ultra-shallow junctions as required in advanced microelectronic technology. Experimental phosphorus dopant diffusion profiles in silicon are described by a rational function diffusion (RFD) model, based on direct solution of Fick’s equations and suitable for actual work in...

2014 The solution of the equation of one-dimensional diffusion with evaporation of the sample and exchange of the diffusant with the ambient at the surface has been applied to the cases of thick layer diffusion, diffusion from an implantation profile and isotope exchange diffusion. Revue Phys. Appl. 24 (1989) 11-16 JANVIER 1989, Classification Physics Abstracts 66.30