##### Venue: Department of Mathematics, Lecture Hall I

We prove the Structure Theorem of the entropy solution. Furthermore we obtain the shock regions each of which represents a single shock at infinity. Using the structure Theorem we construct initial data $u_0\\in C_c^\\f$ for which the solution exhibits infinitely many shocks as $t \\rightarrow \\f$. Also we have generalized the asymptotic behavior (the work of Dafermos, Liu, Kim) of the solution and obtain the rate of decay of the solution with respect to the $N$-wave.

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Last updated: 06 Mar 2020