# PDEMOC14

From Example Problems

Consider with the IC .

Show that a shock develops at a finite time and describe the weak solution.

The chracteristic line is .

To see this, note that the characteristics are so and .

Examine the middle of the region.

For ,

Now we know

.

So is the shock and the characteristics intersect at . Next we'd like to define (in this case) so that the pde is in the form .

The jump condition taken from the far left side to the far right side is:

Plug in the shock to get .

Finally, .

The weak solution is .

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