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MathGroup Archive 2005

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Imposing boundary condition at infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63228] Imposing boundary condition at infinity
  • From: dkjk at bigpond.net.au
  • Date: Mon, 19 Dec 2005 07:02:04 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi all,

I need to solve a differential equation whose solution has the
contraint that it tends to zero in the infinite limit. Mathematica will
not, however, allow \[Phi][Infinity]==0 as one of the contraints. Does
mathematica have another notation for dealing with this constraint?

Thanks.

James

\!\(DSolve[{\(1\/r\^2\) D[r\^2*D[Ï?[r], r],
            r] == \(1\/ϵ\) \((Ï?[r] \((\(2*ec^2*n0\)\/\(k*T\))\) +
\(27*
            q\)\/\(2*Pi*
            a\^3*\@\(2*Pi\)\)*
                Exp[\(-\(\(9  r^2\)\/\(2  a^2\)\)\)])\), Ï?[0] ==
\(\(3\ \@2\ \
q\ λ\)\/Ï?\^\(3/2\) - \(\[ExponentialE]\^\(a\^2\/\(18\ λ\^2\)\)\ q\ \
\@\(a\^2\/λ\^2\)\ λ\)\/Ï? + \(a\ \[ExponentialE]\^\(a\^2\/\(18\
λ\^2\)\)\
                    q\ Erf[a\/\(3\ \@2\ λ\)]\)\/
        Ï?\)\/\(4\ a\ ϵ\ λ\), Ï?[Infinity] == 0}, Ï?, r]\)


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