Initial-boundary value problems for second order systems of partial differential equations

Understand

We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role.

• Attempts have previously been made to write a second order system consisting of n equations as a larger first order system.
• Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger first order system.
• Here we will use the theory of pseudo-differential operators combined with mode analysis.