Applied Maths Workshop: Kennedy -- Applications of test functions and weak solutions to PDEs

ABSTRACT: Test functions are an important tool used to study various equations, allowing
one to make explicit estimates and computations.  I will introduce them and give some
examples of this for Laplace’s equation.  Test functions are also used to define weak
solutions, which can be defined for every PDE (and ODE), and which in some cases provide
the best framework in which to study an equation.  I will illustrate this with a
nonlinear first order PDE which models the formation and propagation of shock waves.  

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ALSO: Dr.  Kennedy will be leaving to take up a research position in Portugal.  We will
be taking him out to farewell drinks after the workshop.  All welcome.