Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation
Applications of Mathematics, Tome 13 (1968) no. 6, pp. 466-477
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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 $c\neq k^2$, $k$ 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.
@article{10_21136_AM_1968_103196,
author = {\v{S}\v{t}astnov\'a, V\v{e}nceslava and Vejvoda, Otto},
title = {Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation},
journal = {Applications of Mathematics},
pages = {466--477},
publisher = {mathdoc},
volume = {13},
number = {6},
year = {1968},
doi = {10.21136/AM.1968.103196},
mrnumber = {0243188},
zbl = {0165.44302},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103196/}
}
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 - Applications of Mathematics PY - 1968 SP - 466 EP - 477 VL - 13 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103196/ DO - 10.21136/AM.1968.103196 LA - en ID - 10_21136_AM_1968_103196 ER -
%0 Journal Article %A Šťastnová, Věnceslava %A Vejvoda, Otto %T Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation %J Applications of Mathematics %D 1968 %P 466-477 %V 13 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1968.103196/ %R 10.21136/AM.1968.103196 %G en %F 10_21136_AM_1968_103196
Šťastnová, Věnceslava; Vejvoda, Otto. Periodic solutions of the first boundary value problem for a linear and weakly nonlinear heat equation. Applications of Mathematics, Tome 13 (1968) no. 6, pp. 466-477. doi: 10.21136/AM.1968.103196
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