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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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