论文标题
关于血管生成的准线性双曲线 - 抛物性模型的不稳定性和稳定性
On instability and stability of a quasi-linear hyperbolic-parabolic model for vasculogenesis
论文作者
论文摘要
在本文中，我们关注的是准线性双曲线 - 羟基蛋白酶系统建模血管网络的不稳定性和稳定性。假设压力满足$ \ frac {νp'（\barρ）} {γ\barρ} <β$，我们首先表明稳态是线性不稳定的（即，线性解决方案在$ l^2 $中的时间增长），通过构建不稳定的解决方案。然后，基于对线性系统解决方案的较低增长估计值，我们证明稳态在Hadamard的意义上是不稳定的。相反，如果压力满足$ \ frac {νp'（\barρ）} {γ\barρ}>β$，我们确定了小扰动的全球存在，并且通过在[liu-peng-peng-wang wang，siam siam siam siam siam J. Math中稍微摆脱条件而略微摆脱了解决方案的全阶衍生率的最佳收敛速率。肛门54：1313--1346，2022]。
In this paper, we are concerned with the instability and stability of a quasi-linear hyperbolic-parabolic system modeling vascular networks. Under the assumption that the pressure satisfies $\frac{νP'(\barρ)}{γ\barρ} < β$, we first show that the steady-state is linear unstable (i.e., the linear solution grows in time in $L^2$) by constructing an unstable solution. Then based on the lower grow estimates on the solution to the linear system, we prove that the steady-state is nonlinear unstable in the sense of Hadamard. On the contrary, if the pressure satisfies $\frac{νP'(\barρ)}{γ\barρ} > β$, we establish the global existence for small perturbations and the optimal convergent rates for all-order derivatives of the solution by slightly getting rid of the condition proposed in [Liu-Peng-Wang, SIAM J. MATH. ANAL 54:1313--1346, 2022].
