Geodesic
Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric
Electronic journal of differential equations, Tome 2005 (2005)
In this paper, we study the solutions to the Cauchy problem

$\displaylines{ (u_{tt}-\Delta u)_{g_s}+m^2u=f(u),\quad t\in (0, 1], x\in \mathbb{R}^3,\cr u(1, x)=u_0\in {\dot B}^{\gamma}_{p, p}(\mathbb{R}^3),\quad u_t(1, x)=u_1\in {\dot B}^{\gamma-1}_{p, p}(\mathbb{R}^3), }$

where

$ u(t,r)= \cases v(t)\omega(r)\\hbox{for }t\in (0, 1],\; r\leq r_1\\ 0\\hbox{for } t\in (0, 1],\; r\geq r_1, \endcases $

where $r=|x|$, and $\lim_{t\to 0}\|u\|_{{\dot B}^{\gamma}_{p, p}(\mathbb{R}^+)}=\infty$.
Classification : 35L05, 35L15
Keywords: partial differential equation, Klein-Gordon, blow up 
@article{EJDE_2005__2005__a24,
     author = {Georgiev,  Svetlin G.},
     title = {Blow up of solutions for {Klein-Gordon} equations in the {Reissner-Nordstrom} metric},
     journal = {Electronic journal of differential equations},
     year = {2005},
     volume = {2005},
     zbl = {1073.35170},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a24/}
}
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TI  - Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric
JO  - Electronic journal of differential equations
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VL  - 2005
UR  - http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a24/
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%0 Journal Article
%A Georgiev,  Svetlin G.
%T Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric
%J Electronic journal of differential equations
%D 2005
%V 2005
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%F EJDE_2005__2005__a24
Georgiev,  Svetlin G. Blow up of solutions for Klein-Gordon equations in the Reissner-Nordstrom metric. Electronic journal of differential equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a24/