The existence of a periodic solution of a parabolic equation with the Bessel operator
Applications of Mathematics, Tome 29 (1984) no. 1, pp. 40-44
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 $a'\in L_\infty (R), h'\in L_\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\cap L_\infty (S,H)$, has the derivative $u'\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.
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 $a'\in L_\infty (R), h'\in L_\infty (R)$ and they fulfil (3). The solution $u$ belongs to the space $L_2(S,V)\cap L_\infty (S,H)$, has the derivative $u'\in L_2(S,H)$ and satisfies the equations (4.1) and (4.2). In the proof the Faedo-Galerkin method is employed.
DOI :
10.21136/AM.1984.104066
Classification :
35B10, 35D05, 35K20
Keywords: diffusion; Bessel operator; periodic solutions; existence; weak solution
Keywords: diffusion; Bessel operator; periodic solutions; existence; weak solution
@article{10_21136_AM_1984_104066,
author = {Lauerov\'a, Dana},
title = {The existence of a periodic solution of a parabolic equation with the {Bessel} operator},
journal = {Applications of Mathematics},
pages = {40--44},
year = {1984},
volume = {29},
number = {1},
doi = {10.21136/AM.1984.104066},
mrnumber = {0729951},
zbl = {0552.35042},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104066/}
}
TY - JOUR AU - Lauerová, Dana TI - The existence of a periodic solution of a parabolic equation with the Bessel operator JO - Applications of Mathematics PY - 1984 SP - 40 EP - 44 VL - 29 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104066/ DO - 10.21136/AM.1984.104066 LA - en ID - 10_21136_AM_1984_104066 ER -
%0 Journal Article %A Lauerová, Dana %T The existence of a periodic solution of a parabolic equation with the Bessel operator %J Applications of Mathematics %D 1984 %P 40-44 %V 29 %N 1 %U http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104066/ %R 10.21136/AM.1984.104066 %G en %F 10_21136_AM_1984_104066
Lauerová, Dana. The existence of a periodic solution of a parabolic equation with the Bessel operator. Applications of Mathematics, Tome 29 (1984) no. 1, pp. 40-44. doi: 10.21136/AM.1984.104066