In this paper, we introduce traveling waves to one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation laws. The equation is regarded as a linear combination of the scalar hyperbolic conservation laws and the porous medium type equations. Thus, this equation has both properties of hyperbolic equations and those of parabolic equations. Accordingly, it is difficult to investigate the behavior of solutions to (CP). Therefore, it is necessary to construct particular solutions and investigate their properties. In pure hyperbolic case, Riemann solutions are well studied because they are self-similar solutions. However, it cannot be expected in this paper. Hence, we focus on the traveling wave structure instead of the self-similar structure.

At first, we construct traveling waves to (CP) and investigate their properties. Next, we discuss the asymptotic behavior of entropy solutions to (CP) using the constructed traveling waves. Finally, we estimate the propagation speed of support for entropy solutions to (CP) using the modified traveling waves.

在本文中，我们将行波引入标量抛物线-双曲守恒律的一维柯西问题（CP）。该方程被视为标量双曲守恒律和多孔介质类型方程的线性组合。因此，该方程具有双曲方程和抛物方程的性质。因此，很难研究（CP）解决方案的行为。因此，有必要构建特定的解决方案并研究其性质。在纯双曲情况下，由于黎曼解是自相似解，因此对其进行了深入研究。但是，这在本文中是无法预期的。因此，我们专注于行波结构而不是自相似结构。

首先，我们构造传播到（CP）的行波并研究其性质。接下来，我们使用构造的行波讨论（CP）熵解的渐近行为。最后，我们使用改进的行波估计对（CP）熵解的支持的传播速度。