论文标题
关于具有非本地边界条件和摩擦阻尼的奇异非线性分数伪型纤维系统的数学模型的良好姿势
On the well posedness of a mathematical model for a singular nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions and frictional damping
论文作者
论文摘要
本文致力于研究单数非线性分数伪hyperbolic系统的适应性。分数衍生物在卡普托意义上描述。这些方程是由经典和非局部边界条件补充的。根据一些先验的估计和密度参数，我们确定了某些Sobolev分数空间中相关线性分数系统的强概括解决方案的存在和唯一性。根据线性分数系统获得的结果，我们应用了一个迭代过程，以建立非线性分数系统的适当性。伪氧化体系统的这种数学模型主要是出于弹性条（梁）的纵向和横向振动的理论，在某些特殊情况下，它以在某些特定边界条件下的两个无限同轴循环圆柱体之间的不稳定螺旋流中提出。
This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the existence and uniqueness of the strongly generalized solution for the associated linear fractional system in some Sobolev fractional spaces. On the basis of the obtained results for the linear fractional system, we apply an iterative process in order to establish the well-posedness of the nonlinear fractional system. This mathematical model of pseudo-hyperbolic systems arises mainly in the theory of longitudinal and lateral vibrations of elastic bars (beams), and in some special case it is propounded in unsteady helical flows between two infinite coaxial circular cylinders for some specific boundary conditions.
