TABLE OF CONTENTS In Chapters 3 to 6 we have assumed spatial periodicity, and Chapter 7 treated the case of one space variable 0 ? x ?1 or 0 ? x< ?. Here we want to combine the two situations and consider a space variable
under periodicity assumptions in x 2, , x s. These special x-domains are fairly representative in the sense that problems posed in other domains (with smooth boundary) can be broken up into subproblems which can be transformed to the special cases.
We consider second-order systems
in the strip.
At time t=0 we give initial data
and at the surfaces
we prescribe linear (inhomogeneous) boundary conditions combining u and D 1 u. Introducing the notation
we can write the boundary conditions in the general form
where L j 0= L j 0 (y, t), L j 1= L j 1 (y,t), j=0,1, are n n matrices. The coefficients A ij =A ij (x, t), etc., the forcing F= F(x,t), the initial function f= f(x) , the inhomogeneous boundary terms g j =g j (y, t), and the coefficients L jv= L jv (y, t) of the boundary conditions are all assumed to be C ?-smooth, 1-periodic with respect to x 2, , x s , and real, for simplicity. The differential equation (8.1.1)...
