Solvability for a drift-diffusion system with Robin boundary conditions

TL;DR

This paper establishes the existence of solutions for a drift-diffusion system with Robin boundary conditions, using L1, L2, and trace estimates, and applies the results to corrosion and self-gravitation models.

Contribution

It provides a general existence theorem for the system with large initial data under Robin boundary conditions, including practical applications.

Findings

Existence of solutions for the drift-diffusion system.

Application to corrosion and self-gravitation models.

Use of L1, L2, and trace estimates for analysis.

Abstract

This paper focuses on a drift-diffusion system subjected to boundedly non dissipative Robin boundary conditions. A general existence result with large initial conditions is established by using suitable L1, L2 and trace estimates. Finally, two examples coming from the corrosion and the self-gravitation model are analyzed.