The well-posedness of bipolar semiconductor hydrodynamic model with recombination-generation rate on the bounded interval

ABSTRACT

We study the initial boundary value problem of bipolar semiconductor hydrodynamic model with recombination-generation rate for the non-constant doping profile. The new feature is that the current distribution for electrons and holes is not constant. In order to overcome this difficulty, the existence and uniqueness of a subsonic stationary solution are first established by elliptic theorem. Then, for such an Euler–Poisson system, we prove, by means of a technical energy method, that the subsonic solutions are unique, exist globally and asymptotically converge to the corresponding stationary solutions. An exponential decay rate is also derived.

KEYWORDS:

• Recombination-generation rate
• global-in-time solution
• subsonic
• energy estimates

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 82D37
• 35M33
• 76N10
• 35B40
• 35Q35

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by National Natural Science Foundation of China (NSFC) (Project 11421061) and by Natural Science Foundation of Shanghai [15ZR1403900].