Finite Time Emergence of a Shock Wave for Scalar Conservation Laws

@inproceedings{Shearer2009FiniteTE,
  title={Finite Time Emergence of a Shock Wave for Scalar Conservation Laws},
  author={M. Shearer and Constantine M. Dafermos},
  year={2009}
}
For a convex conservation law ut + f(u)x = 0, u(x, 0) = u0(x), −∞ < x <∞, t > 0, bounded initial data u0(x), are considered that take on constant values u− to the left of a bounded interval, and u+ to the right, with u− > u+. The solution of the initial value problem is shown to collapse in finite time to a single shock wave joining u− to u+. The proof involves comparison with a solution having piecewise constant initial data for which the time of collapse is be calculated explicitly. This… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 12 references

Dafermos, Large time behaviour of solutions of hyperbolic balance laws

C M.
Bull. Greek Math. Soc • 1984
View 1 Excerpt

Large time behaviour of solutions of hyperbolic balance laws , Bull

C. M. Dafermos
Greek Math . Soc . • 1984

Characteristics in hyperbolic conservation laws. A study of the structure and asymptotic behavior of solutions

C. M. Dafermos
Nonlinear Analysis and Mechanics, • 1977
View 1 Excerpt

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