Multi-dimensional Riemann problem of scalar conservation law

This paper considers multi-dimensional Riemann problem in another kind of view. The author gets solution of (1.1)(1.2) in Theorem 3.4 and proves itu uniqueness. A new method of solution constructing is applied, which is different from the usual self-similar transformation. The author also discusses some generalized concepts in multi-dimensional situation (such as "convex condition", "left value" and "right value", etc). An example is finally given to demonstrate that rarefaction wave solution of (1.1)(1.2) is not self-similar.