331423969

The variational formulation of the above coupled system reads:

Problem

Find u G V and q G Q such that G V, G Qo,

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[ <r(u) • V^s7y — [ ku-Tj+ f S(w. q) • V^sr/ = 0

Jn^M    J r* Jęi^p

I c!)(w.q)    = 0

Jq.p

where u = u in Q^M and u = w in ft^p,

V = {veH¹(Q) :v|_ro = 0} , while the electric potentials sets Q. Q₀ C H¹(Q^p)

Q {<łlr <)• <7lr₀ = °} •2o = {<7ls_np = 0} .

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		. □ .	—143” ■ U' <s> a <00.0
J. Sokołowski (IECL)	Topological Derivatives		October 6, 2015 41 / 110