【摘 要】
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We discuss the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one-dimensional heatconductive hy
【机 构】
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DepartmentofMathematicalandComputingSciences,TokyoInstituteofTechnology,Japan
【出 处】
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International Conference on Nonlinear PDEs and Their Applica
论文部分内容阅读
We discuss the existence and the asymptotic stability of a stationary solution to the initial boundary value problem for a one-dimensional heatconductive hydrodynamic model for semiconductors ρt + jx =0,(1a)jt +(j2/ρ+ P(ρ,θ)x =ρφx-j/Υm,(lb)ρθt+jθx+3/ 2(j/ρ)xρθ-2/3(κθx)x=vj2/ρ-ρ/Υe(θ-(θ)),(1c)φxx =ρ-D,(ld)for x ∈Ω:=(0,1).Here,the unknown functions ρ,j,θ and φ stand for electron density,electric current,absolute temperature and electrostatic potential,respectively.The positive constants (θ),κ,τ,m and τe mean ambient device temperature,thermal conductivity,momentum relaxation time and energy relaxation time,respectively.Moreover,the constant v is equal to (2Te-Tm)/τmTe.The pressure p is assumed that p =p(ρ,θ) =ρθ.
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