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Lieberman, Gary M.

Time-periodic solutions of linear parabolic differential equations. (English) Zbl 0928.35012

Commun. Partial Differ. Equations 24, No. 3-4, 631-663 (1999).
This paper concerns general linear nonhomogeneous second order parabolic equations on possibly non-cylindrical domains and with possibly nonhomogeneous Dirichlet or oblique derivative boundary conditions. The author proves several results of the Fredholm alternative type for time-periodic solutions for equations in non-divergence form (classical solutions in the case of Hölder continuous coefficients and strong solutions in the case of continuous highest order coefficients) as well as for divergence form equations \((L^\infty\)-coefficients and weak solutions). Also there are added some new results involving weakened regularity hypotheses on the coefficients and an excellent survey on related results concerning existence, uniqueness and a priori estimates of time-periodic solutions and compactness in the corresponding function spaces.
Reviewer: L.Recke (Berlin)

Cited in 1 Review
Cited in 16 Documents

MSC:

35B10 Periodic solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
47A53 (Semi-) Fredholm operators; index theories
35D10 Regularity of generalized solutions of PDE (MSC2000)

Keywords:

classical solutions; non-cylindrical domains; nonhomogeneous Dirichlet or oblique derivative boundary conditions; Fredholm alternative; non-divergence form; strong solutions; divergence form; weak solutions
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References:

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