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On the local existence of C^1 solutions for the initial value problem of the 1D linear hyperbolic system of conservation laws

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If you have a question about this talk, please contact Renato Velozo.

Hyperbolic partial differential equations play an important role in physics, especially in continuum mechanics. The flow of gases governed by the Euler equation is a typical example of hyperbolic PDEs. In this talk, we will be concerned with local well-posedness of some one-dimensional linear hyperbolic system of equations. We will show using the fixed point iteration method, that given an initial data continuously differentiable, there exists a unique continuously differentiable solution to our hyperbolic PDEs up to some finite time t>0.

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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