论文标题
对扰动非线性传输方程的测量解决方案参数的存在和可不同的性能
Existence and differentiability in parameter of the measure solution to a perturbed non-linear transport equation
论文作者
论文摘要
我们考虑在非线性传输方程中对措施的扰动，即初始条件$μ_0$和解决方案$μ_t^h $都是界限的radon测度$ \ MATHCAL {M}（\ MATHBBBB {r}^d）$。扰动发生在速度场以及右侧标量函数中。结果表明，对于扰动参数$ h $，即该衍生物是适当的Banach空间的元素。该结果扩展了我们先前考虑线性传输方程的结果。证明利用了基于线性方程的研究的非线性问题的近似。
We consider a perturbation in the non-linear transport equation on measures i.e. both initial condition $μ_0$ and the solution $μ_t^h$ are bounded Radon measures $\mathcal{M}(\mathbb{R}^d)$. The perturbations occur in the velocity field and also in the right-hand side scalar function. It is shown that the solution is differentiable with respect to the perturbation parameter $h$ i.e. that derivative is an element of a proper Banach space. This result extends our previous result which considered the linear transport equation. The proof exploits approximation of the non-linear problem which is based on the study of the linear equation.
