论文标题
消失的粘度限制的显式结构，其初始数据由$δ$ - 分布组成，从两个点源开始
Explicit structure of the vanishing viscosity limits with initial data consisting of $δ$-distributions starting from two point sources
论文作者
论文摘要
在本文中，我们考虑了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平面中具有两种线性组合u_a \δ_{x = a} + u_b \δ_{x = b}，\ρ| _ {t = 0} =ρ_C\δ__{x = c} +ρ_d\δ__{x = d} \]作为初始数据。这里$ a $，$ b $，$ c $，$ d $是订购为$ a <c <b <d $的实际点的不同积分。我们的目标是利用相应的修改后的粘附模型\ [u^ε_t + \ left（{（u^ε）^2}/{2} \ right）_x = \fracε_________________ （ρ^εu^ε）_x = \fracε{2}ρ^ε_{xx}。为此，我们广泛使用函数erfc $的各种渐近性属性：z \ longmapsto \ int_ {z}^{\ infty} e^{ - s^2} \ ds $以及合适的hopf-cole转换。
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 two $δ$-distributions \[ u|_{t=0} = u_a\ δ_{x=a} + u_b\ δ_{x=b},\ ρ|_{t=0} = ρ_c\ δ_{x=c} + ρ_d\ δ_{x=d} \] as initial data. Here $a$, $b$, $c$, $d$ are distinct points on the real line ordered as $a < c < b < d$. Our objective is to provide a detailed analysis of the structure of the vanishing viscosity limits of this 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 extensively use the various asymptotic properties of the function erfc$: z \longmapsto \int_{z}^{\infty} e^{-s^2}\ ds$ along with suitable Hopf-Cole transformations.
