一类非线性退化半导体方程弱解存在性的研究

Existence of solutions on a quasilinear degenerate system arising in semiconductors theory

目的研究非线性退化半导体方程在初值u0,v0∈L2+(Ω)的条件下,其混和初边值问题弱解的存在性。方法利用截断的方法先将原问题正则化,对正则化问题的解做估计,并利用紧性引理。结果通过取极限证明了原问题解的存在性。结论在满足一定假设条件下,非线性退化半导体方程存在弱解。

Aim To prove the existence of the weak solution under appropriate conditions such as initial values u0,v0∈L2＋（Ω） when a quasilinear degenerate system arising in semiconductors theory is considered. Methods Make a regularization of the problem by a cut-off method and the compact lemma. Results The limit of the solutions of the regularized problem is a solution of the original problem after estimates. Conclusion The existence of solutions on a quasilinear degenerate system is shown under some conditions.