Local Existence Result of the Dopant Diffusion in Arbitrary Space Dimensions

Local Existence Result of the Single Dopant Diffusion including Cluster Reactions of High Order

We consider the pair diffusion process which includes cluster reactions of high order. We are able to prove a local (in time) existence result in arbitrary space dimensions. The model includes a nonlinear system of reaction-drift-diffusion equations, a nonlinear system of ordinary differential equations in Banach spaces, and a nonlinear elliptic equation for the electrochemical potential. The l...

Local Existence Result of the Single Dopant Diffusionin Arbitrary Space Dimensions

The Single Dopant Diffusion in Arbitrary Space Dimension

In this paper we consider the pair di usion process in more than two spatial dimensions. In this case we are able to prove just a local existence result, since it is not possible to deduce global a priori estimates for the equations as it can be done in the two dimensional case. The model includes a nonlinear system of reaction{ drift{di usion equations, a nonlinear ordinary di erential equatio...

Modeling of Manufacturing of Field-Effect Heterotransistors without P-n-junctions to Optimize Decreasing their Dimensions

It has been recently shown that manufacturing p-n-junctions, field-effect and bipolar transistors, thyristors in a multilayer structure by diffusion or ion implantation with the optimization of dopant and/or radiation defects leads to increase the sharpness of p-n-junctions (both single p-n-junctions and p-n-junctions framework their system). Due to the optimization, one can also obtain increas...

Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion

Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification and generalization of the well-posedness theory of these models. We prove local well-posedness on bounded domains for dimensions d ≥ 2 and in all of space for d ≥ 3, the uniqueness being a result ...