论文标题
由特征函数的线性组合和$δ$分布的零压力气体动力学系统的消失粘度限制的显式结构
Explicit structure of the vanishing viscosity limits for the zero-pressure gas dynamics system initiated by the linear combination of a characteristic function and a $δ$-distribution
论文作者
论文摘要
在本文中，我们考虑一维零压力动力学系统\ [u_t + \ left（{{u^2}/{2}/{2} \ right）_x = 0，\ρ_t +（ρ_t +（ρu）_x = 0 \]在上half平面中，在上half平面中具有线性函数和特征性功能和$Δ$ | | u_a \χ_{{} _ {\ left（ - \ infty，a \ right）}}} + u_b \δ_{x = b}，\ρ| _ {t = 0} = 0} =ρ_C\χ_{} δ_{x = d} \]作为初始数据，其中$ a $，$ b $，$ c $，$ d $是订购为$ a <c <b <d $的实际线的不同点，并提供了对上述系统消失的粘度限制的详细分析，用于上述系统利用相应的修改后的粘附模型/ \ right）_x = \fracε{2} u^ε_{xx}，\ρ^ε_t +（ρ^εu^ε）_x = \fracε{2}ρ^ε_________________{xx}。为此，我们使用函数ERFC $的合适的Hopf-Cole转换和各种渐近属性：z \ longmapsto \ int_ {z}^{\ infty} {\ infty} e^{ - s^2} \ ds $。
In this article, we consider the one-dimensional zero-pressure gas dynamics system \[ u_t + \left( {u^2}/{2} \right)_x = 0,\ ρ_t + (ρu)_x = 0 \] in the upper-half plane with a linear combination of a characteristic function and a $δ$-measure \[ u|_{t=0} = u_a\ χ_{ {}_{ \left( -\infty , a \right) } } + u_b\ δ_{x=b},\ ρ|_{t=0} = ρ_c\ χ_{ {}_{ \left( -\infty , c \right) } } + ρ_d\ δ_{x=d} \] as initial data, where $a$, $b$, $c$, $d$ are distinct points on the real line ordered as $a < c < b < d$, and provide a detailed analysis of the vanishing viscosity limits for the above system utilizing the corresponding modified adhesion model \[ u^ε_t + \left({(u^ε)^2}/{2} \right)_x =\fracε{2} u^ε_{xx},\ ρ^ε_t + (ρ^εu^ε)_x = \fracε{2} ρ^ε_{xx}. \] For this purpose, we use suitable Hopf-Cole transformations and various asymptotic properties of the function erfc$: z \longmapsto \int_{z}^{\infty} e^{-s^2}\ ds$.
