Solution to a 2-Dimensional Burgers Equation With Initial Discontinuity on Two Concentric Circles

The shock wave, rarefaction wave and their global structure of interactions to 2-D Burgers equation with initial discontinuity were obtained based on two concentric circles with different radii. When the initial data just contained two different constant states, through condition H(H') and condition R-H, solutions were given respectively when 0 \leqslant t \leqslant \frac2\sqrt 2 u_ + - u_ - ,\frac2\sqrt 2 u_ + - u_ - < t \leqslant \frac4u_ + - u_ - ,\frac4u_ + - u_ - < t \leqslant \frac8u_ + - u_ - ,\frac8u_ + - u_ - < t \leqslant \frac2\left( \sqrt 26 - 7\sqrt 2 - \sqrt 10 - 7\sqrt 2 \right)u_ + - u_ - ,\frac2\left( \sqrt 26 - 7\sqrt 2 - \sqrt 10 - 7\sqrt 2 \right)u_ + - u_ - < t \leqslant \frac6\sqrt 2 + 8u_ + - u_ - and t > \frac6\sqrt 2 + 8u_ + - u_ - and some new phenomena were discovered. Finally, the structure of global solution which had the special structure for any fixed time "t" was presented.