论文标题
非线性玻尔兹曼方程中碰撞内核的重建
Reconstruction of the collision kernel in the nonlinear Boltzmann equation
论文作者
论文摘要
我们认为，在尺寸为$ n \ geq 2 $的玻尔兹曼方程的逆问题。我们表明，只要内核满足单调性条件，动力学碰撞内核就可以从域边界上的到达映射中唯一确定。此外，还得出了重建公式。关键方法基于高阶线性化方案，通过将多个小参数引入原始方程中，将非线性方程式降低到更简单的线性方程中。
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary of the domain provided that the kernel satisfies a monotonicity condition. Furthermore, a reconstruction formula is also derived. The key methodology is based on the higher-order linearization scheme to reduce a nonlinear equation into simpler linear equations by introducing multiple small parameters into the original equation.
