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This is probably a stupid question but I have Neumann BC boundary : ## \nabla u . \vec{n} =0## (same for ##v##)conditions for the following reactiondiffusion system on a [0,L_1]x[0,L_2]x...x...[0,L_n] n times in n dimensional space so ##u=u(x_1,.....,x_n,t)## is a scalar I believe?
so that ## \nabla u . \vec{n} ## is a vector times a vector is a scalar,
my notes then say:
and so, I'm confused how to argue, from, a summation of ##u_i## derivatives we conclude that each ##u_i## derivative must individually be zero? unless we are specifying ##n## different normal vectors, one for each surface (divided by two for the what would be a negative of this normal vector) ? so like ##(1,0....0)## ,...,(0,0,.....1) ##
ahh this must be the case actually and i have misinterpreted the boundary condition?? thanks
so that ## \nabla u . \vec{n} ## is a vector times a vector is a scalar,
my notes then say:
and so, I'm confused how to argue, from, a summation of ##u_i## derivatives we conclude that each ##u_i## derivative must individually be zero? unless we are specifying ##n## different normal vectors, one for each surface (divided by two for the what would be a negative of this normal vector) ? so like ##(1,0....0)## ,...,(0,0,.....1) ##
ahh this must be the case actually and i have misinterpreted the boundary condition?? thanks
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