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Periodic solutions of singular linear and semilinear parabolic problems

1989; Brown University; Volume: 47; Issue: 3 Linguagem: Inglês

10.1090/qam/1012266

1552-4485

C. Y. Chan, Benedict M. Wong,

Numerical methods for differential equations

1. Introduction.Let Lc be the singular second-order parabolic differential operator defined by b Lcu = uxx H-ux + c(t)u -ut, X where the constant b < 1 and c{t) < 0. Recently, Chan and Chen [4] studied quenching phenomena involving L0 subject to zero initial data and zero first boundary conditions.The significance of the operator Lq is also discussed there.Here, we would like to study periodic solutions for both linear and semilinear problems involving Lc subject to first boundary conditions.Periodic solutions for the special case b = 0 have been studied by many investigators; some more recent results have been obtained by Chan and Wong [5], where further references can be found.In this work, we are interested in time-periodic solutions of period T (namely, T-periodic solutions).We start with investigating the following linear problem: Lku = -X¥(x,t) in Qoo, (1.1)