Du, Q. and Gunzburger, M. and Lehoucq, R. B. and Zhou, K. (2011) A nonlocal vector calculus,nonlocal volumeconstrained problems,and nonlocal balance laws. Mathematical Models and Methods in Applied Sciences . (Submitted)

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Abstract
A vector calculus for nonlocal operators is developed, including the definition of nonlocal divergence, gradient, and curl operators and the derivation of the corresponding adjoints operators. Nonlocal analogs of several theorems and identities of the vector calculus for differential operators are also presented. Relationships between the nonlocal operators and their differential counterparts are established, first in a distributional sense and then in a weak sense by considering weighted integrals of the nonlocal adjoint operators. The nonlocal calculus gives rise to volumeconstrained problems that are analogous to elliptic boundaryvalue problems for differential operators; this is demonstrated via some examples. Another application is posing abstract nonlocal balance laws and deriving the corresponding nonlocal field equations.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  1437 
Deposited By:  Peter Hudston 
Deposited On:  18 Nov 2011 07:42 
Last Modified:  29 May 2015 19:08 
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