Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation

Šťastnová, Věnceslava, and Vejvoda, Otto. "Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation." Aplikace matematiky 13.6 (1968): 466-477. <http://eudml.org/doc/14568>.

@article{Šťastnová1968,
abstract = {One investigates the existence of an $\omega $-periodic solution of the problem $u_t=u_\{xx\}+cu+g(t,x)+\epsilon f(t,x,u,u_x,\epsilon ),\ u(t,0)=h_0(t)+\epsilon \chi _0(t,u(t,0),u(t,\pi )), u(t,\pi )=h_1(t)+\epsilon \chi _1(t,u(t,0), u(t,\pi ))$, provided the functions $g,f,h_0,h_1,\chi _0,\chi _1$ are sufficiently smooth and $\omega $-periodic in $t$. If $c\ne k^2$, $k$ natural, such a solution always exists for sufficiently small $\epsilon >0$. On the other hand, if $c=l^2$, $l$ natural, some additional conditions have to be satisfied.},
author = {Šťastnová, Věnceslava, Vejvoda, Otto},
journal = {Aplikace matematiky},
keywords = {partial differential equations},
language = {eng},
number = {6},
pages = {466-477},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation},
url = {http://eudml.org/doc/14568},
volume = {13},
year = {1968},
}

TY - JOUR
AU - Šťastnová, Věnceslava
AU - Vejvoda, Otto
TI - Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation
JO - Aplikace matematiky
PY - 1968
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 13
IS - 6
SP - 466
EP - 477
AB - One investigates the existence of an $\omega $-periodic solution of the problem $u_t=u_{xx}+cu+g(t,x)+\epsilon f(t,x,u,u_x,\epsilon ),\ u(t,0)=h_0(t)+\epsilon \chi _0(t,u(t,0),u(t,\pi )), u(t,\pi )=h_1(t)+\epsilon \chi _1(t,u(t,0), u(t,\pi ))$, provided the functions $g,f,h_0,h_1,\chi _0,\chi _1$ are sufficiently smooth and $\omega $-periodic in $t$. If $c\ne k^2$, $k$ natural, such a solution always exists for sufficiently small $\epsilon >0$. On the other hand, if $c=l^2$, $l$ natural, some additional conditions have to be satisfied.
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/14568
ER -