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Conservation laws for physical problems often yield important physical
insight, like for example, the conservation of energy or Bernoulli's law.
They can also yield time decay laws for solutions of hyperbolic p.d.e.
In this talk we shall begin with simple linear and nonlinear examples
which under a stretching of the independent variables produce another
solution.One can then obtain time decay from the usual energy estimate.
But more general examples of time decay based on invariance are found by
Noether's theorem. From there one can move to some 2D results for equations
that are not necessarily hyperbolic such as the Tricomi equation, the
hyperbolic wave equation and also Born Infeld equations.
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