# Reference request on connection between PDE problems

I am trying to find references in the literature that connect solutions of any two of the problems given bellow. I study deterministic and stochastic conservation laws. Problems that I am interested in are:

Deterministic Cauchy problem: $$\hspace{1cm} (1) \hspace{1cm} \begin{cases} u_t+f(u)_x=0 \\[2ex] u(x,0)=u_0 (x) \end{cases}$$

Deterministic Riemann problem: $$\hspace{1cm} (2) \hspace{1cm} \begin{cases} u_t+f(u)_x=0 \\[2ex] u(x,0)= \begin{cases} u_l, x<0 \\[2ex] u_r, x\geq0 \end{cases} \end{cases}$$

Stochastic Riemann problem: $$\hspace{1cm} (3) \hspace{1cm} \begin{cases} u_t+f(u)_x=g(u)W(t) \\[2ex] u(x,0)= \begin{cases} u_l, x<0 \\[2ex] u_r, x\geq0 \end{cases} \end{cases}$$

Stochastic Cauchy problem: $$\hspace{1cm} (4) \hspace{1cm} \begin{cases} u_t+f(u)_x=g(u)W(t) \\[2ex] u(x,0)=u_0 (x) \end{cases}$$

Here u $$\in \mathbb{R}^n$$ and W(t) is a white noise. For $$n=1$$ we have one equation and for $$n>1$$ we have system of conservation laws. Function $$g$$ depends of $$u$$ so we say that we have multiplicative noise.

So far I only have found two references that study connection between solutions of problems (1) and (2). Those are:

1. TP Liu, Large-Time Behavior of Solutions of Initial and Initial-Boundary Value Problems of a General System of Hyperbolic Conservation Laws, Comm. Math. Phys. Volume 55, Number 2 (1977), 163-177; projecteuclid, DOI: 10.1007/BF01626518.
2. L. Hsiao, Quasilinear hyperbolic systems and dissipative mechanisms, World Scientific Publishing, 1997 - Chapter 5.

Anyone know any reference that connects any other pair of problems?