Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity by Alexander A. Lokshin

Author:Alexander A. Lokshin
Language: eng
Format: epub
ISBN: 9789811585784
Publisher: Springer Singapore

Corollary

Suppose the relaxation kernel R(t) can be represented in the form

where ∣ai∣ are increasing not so rapidly as a geometrical progression. Then the wave operator with memory

is hyperbolic in S'. In fact, for this operator

Theorem 2.2.4

Let V0 be strictly hyperbolic, and suppose

Then all the assertions of the previous theorem hold true for the space D'.

Proofs of these theorems are similar to the proofs of the corresponding assertions for operators containing a single convolution (see Theorems 2.1.1 and 2.1.3). Conditions of hyperbolicity given in Theorems 2.2.3 and 2.2.4 are close to necessary and sufficient ones. It is possible to specify these results in dependence on the character of growth of ϕ(t)  as  t → + 0.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.