The Eigenfrequency Spectra of the Interior Problems
As we saw in the previous chapter, each of the exterior boundary value problems has at most one regular solution. Unfortunately, this is not true for (Dω+) and (Nω+). We prove that (D0ω+) and (N0ω+) have nonzero solutions by establishing their equivalence to certain integral equations that are known to have such solutions. To do so, we construct the kernels of these integral equations—the so-called Green’s tensors. Throughout the chapter we exploit the close connection between system (4.1) and the corresponding homogeneous system governing the equilibrium bending of plates.
KeywordsIntegral Equation Regular Solution Boundary Integral Equation Representation Formula Homogeneous Problem
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