Two-point boundary value problems for linear evolution equations

Source abstract

We study boundary value problems for a linear evolution equation with spatial derivatives of arbitrary order, on the domain 0 < x < L , 0 < t < T , with L and T positive finite constants. We present a general method for identifying well-posed problems, as well as for constructing an explicit representation of the solution of such problems. This representation has explicit x and t dependence, and it consists of an integral in the k -complex plane and of a discrete sum. As illustrative examples we solve some two-point boundary value problems for the equations iq t + q xx = 0 and q t + q xxx = 0.