Existence and uniqueness of stationary solutions to a one-dimensional bipolar hydrodynamic model of semiconductors

Global existence and asymptotic behavior of the solutions to the 3D bipolar non-isentropic Euler–Poisson equation

“…Recently, many efforts were made for the isentropic bipolar hydrodynamic equations from semiconductors or plasmas. Zhou and Li [25] and Tsuge [22] discussed the unique existence of the stationary solutions for the one-dimensional bipolar hydrodynamic model with proper boundary conditions. Natalini [18] and Hsiao and Zhang [6] established the global entropy weak solutions in the framework of compensated compactness on the whole real line and bounded domain respectively.…”

Global existence and asymptotic behavior of smooth solutions for a bipolar Euler-Poisson system in the quarter plane

“…More precisely, Zhou and Li [4] and Tsuge [5] discussed the unique existence of the stationary solutions for the one-dimensional bipolar hydrodynamic model with proper boundary conditions. Natalini [6], and Hsiao and Zhang [7,8] established the global entropic weak solutions in the framework of compensated compactness on the whole real line and spatial bounded domain respectively.…”

Asymptotic convergence to planar stationary waves for multi-dimensional unipolar hydrodynamic model of semiconductors

“…The study on hydrodynamical system of semiconductor devices has been one of hot spots of research in mathematical physics, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] and the references therein. Among them, the most studies are related only to the 1-D case, and the study to the n-D case is very limited.…”

“…Among them, the most studies are related only to the 1-D case, and the study to the n-D case is very limited. For the unipolar isentropic and nonisentropic hydrodynamical equations of semiconductors (one carrier type) in 1-D case, Degond and Markowich [3,4], Fang and Ito [5], Gamba [6], Tsuge [33], and Nishibata and Suzuki [29] investigated the existence and uniqueness of (subsonic) 1-D stationary solutions. Such stationary solutions are also called the (planar) stationary waves to the original equations (1.1).…”