The Vlasov–Poisson–Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani–Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $$L^\infty $$ L ∞ -estimate and $$W^{1,p}$$ W 1 , p -estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani–Lampis boundary for the $$L^\infty $$ L ∞ -estimate, and an intrinsic decomposition of boundary integral for $$W^{1,p}$$ W 1 , p -estimate.

中文翻译：

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具有广义扩散边界条件的 Vlasov-Poisson-Boltzmann 方程的局部适定性

Vlasov-Poisson-Boltzmann 方程是控制带电粒子动力学的经典方程，其中的电力是自加的。我们在具有 Cercignani-Lampis 边界条件的凸域中考虑系统。我们基于 $$L^\infty $$ L ∞ -estimate 和 $$W^{1,p}$$ W 1 , p -estimate 构建唯一性本地时间解决方案。特别是，我们开发了一个新的迭代方案，沿着具有 Cercignani-Lampis 边界的 $$L^\infty $$ L ∞ 估计的特征，以及 $$W^{1,p} 的边界积分的内在分解$$ W 1 ，p 估计。