On a drift-diffusion system for semiconductor devices

Abstract

In this note we study a fractional Poisson-Nernst-Planck equation modeling a semiconductor device. We prove several decay estimates for the Lebesgue and Sobolev norms in one, two and three dimensions. We also provide the first term of the asymptotic expansion as $t\to \infty$.

to appear in Annales Henri Poincaré

References in corpus (6)

• The fractional Keller-Segel model
• Global solutions for a supercritical drift-diffusion equation
• Global existence for diffusion-electromigration systems in space dimension three and higher
• Exponential convergence to equilibrium in a Poisson-Nernst-Planck-type system with nonlinear diffusion
• The Optimal Temporal Decay Estimates for the Fractional Power Dissipative Equation in Negative Besov Spaces
• Well-posedness and Gevrey Analyticity of the Generalized Keller-Segel System in Critical Besov Spaces

Cited by in corpus (3)

• The Optimal Temporal Decay Estimates for the Fractional Power Dissipative Equation in Negative Besov Spaces
• Suppression of blow up by a logistic source in $2$D Keller-Segel system with fractional dissipation
• Suppression of blow up by mixing in generalized Keller-Segel system with fractional dissipation