The existence of a periodic solution of a parabolic equation with the Bessel operator

Lauerová, Dana. "The existence of a periodic solution of a parabolic equation with the Bessel operator." Aplikace matematiky 29.1 (1984): 40-44. <http://eudml.org/doc/15331>.

@article{Lauerová1984,
abstract = {In this paper, the existence of an $\omega $-periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions $f(t,r),h(t),a(t)$ are assumed to be $\omega $-periodic in $t,f\in L_2(S,H),a,h$ such that $a^\{\prime \}\in L_\infty (R), h^\{\prime \}\in L_\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\cap L_\infty (S,H)$, has the derivative $u^\{\prime \}\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.},
author = {Lauerová, Dana},
journal = {Aplikace matematiky},
keywords = {diffusion; Bessel operator; periodic solutions; existence; weak solution; diffusion; Bessel operator; periodic solutions; existence; weak solution},
language = {eng},
number = {1},
pages = {40-44},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The existence of a periodic solution of a parabolic equation with the Bessel operator},
url = {http://eudml.org/doc/15331},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Lauerová, Dana
TI - The existence of a periodic solution of a parabolic equation with the Bessel operator
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 1
SP - 40
EP - 44
AB - In this paper, the existence of an $\omega $-periodic weak solution of a parabolic equation (1.1) with the boundary conditions (1.2) and (1.3) is proved. The real functions $f(t,r),h(t),a(t)$ are assumed to be $\omega $-periodic in $t,f\in L_2(S,H),a,h$ such that $a^{\prime }\in L_\infty (R), h^{\prime }\in L_\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\cap L_\infty (S,H)$, has the derivative $u^{\prime }\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.
LA - eng
KW - diffusion; Bessel operator; periodic solutions; existence; weak solution; diffusion; Bessel operator; periodic solutions; existence; weak solution
UR - http://eudml.org/doc/15331
ER -