Geodesic
On a Phragmen–Lindelöf type theorem in the strip
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 115-127 
I. I. Antypko. On a Phragmen–Lindelöf type theorem in the strip. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2001) no. 2, pp. 115-127. http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a0/
@article{JMAG_2001_8_2_a0,
     author = {I. I. Antypko},
     title = {On a {Phragmen{\textendash}Lindel\"of} type theorem in the strip},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {115--127},
     year = {2001},
     volume = {8},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a0/}
}
TY  - JOUR
AU  - I. I. Antypko
TI  - On a Phragmen–Lindelöf type theorem in the strip
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2001
SP  - 115
EP  - 127
VL  - 8
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a0/
LA  - ru
ID  - JMAG_2001_8_2_a0
ER  - 
%0 Journal Article
%A I. I. Antypko
%T On a Phragmen–Lindelöf type theorem in the strip
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2001
%P 115-127
%V 8
%N 2
%U http://geodesic.mathdoc.fr/item/JMAG_2001_8_2_a0/
%G ru
%F JMAG_2001_8_2_a0

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $u(x,t)$ be a solution of the equation $\frac{\partial^2u(x,t)}{\partial t^2}+Q\left(\frac{\partial}{\partial x}\right)u(x,t)=0$ in the strip $\Pi(T)=\left\{(x,t):x\in\mathbb R\land t\in [0,T]\right\}$, where $Q(s)$ is an arbitrary polynomial with respect to $s\in\mathbb C$ with constant complex coefficients. In the paper the dependence of the behavior of $u(x,t)$ on the functions $$ u_1(x)=u(x,0), \quad u_2(x)=\frac{\partial u(x,T)}{\partial t} $$ or $$ u_1(x)=\frac{\partial u(x,0)}{\partial t},\quad u_2(x)=u(x,T), $$ at infinity is studied.