Geodesic
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.

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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 
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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. http://geodesic.mathdoc.fr/articles/10.21136/AM.1984.104066/

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