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]\)