Progress in Partial Differential Equations by Michael Reissig & Michael Ruzhansky

Author:Michael Reissig & Michael Ruzhansky
Language: eng
Format: epub
Publisher: Springer International Publishing, Heidelberg

and evaluate the derivatives of the function (24):

By setting t=T=4ℓ(n+1) and by using the terminal conditions (25), we obtain

The half-sum and half-difference of the last two relations provide constraints for all x in the interval [0,ℓ]:

(26)

(27)

Relations (26) and (27) are equalities of elements of the class L p [0,ℓ]. In addition, note that if x is replaced by 2ℓ−x, then, by taking into account the odd extension of φ(x) and ψ(x) around the point x=ℓ, one reduces relation (27) to (26) expressed for all x in the interval [ℓ,2ℓ]. Consequently, relation (26) should be treated as an equality of elements of the class L p [0,2ℓ].

We perform the substitution m=2n−k+2 in the first sum and m=2n−k+1 in the second sum of relation (26):

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.