On Solution to Riemann Problem in Logarithmic Cases

The article is devoted to an extended application of the logarithmization method to the study of solvability of the Riemann problem. Here we deal with solution of the Riemann problem for two functions and use the logarithmization method to the product of \(2\times 2\) nonsingular matrices. It is proved that this method is applicable to monodromy matrices with any Jordan normal form. Using this fact we solve the Riemann problem in the so called logarithmic cases.