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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 813-828, October 2007




A FOURTH ORDER DEGENERATE PARABOLIC EQUATION

WITH $ p(x)$-GROWTH CONDITIONS


BY


CHANGCHUN LIU AND TIEZHU LI




Abstract. We consider an initial-boundary value problem for a fourth order degenerate parabolic equation with $ p(x)$-growth conditions. Under some assumptions on the initial value, we establish the existence of weak solutions by the time-discrete method. The uniqueness and asymptotic behavior of solutions are also discussed.

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Received September 13, 2006.

AMS Subject Classification. 35D05, 35B40, 35G30, 35K55.

Key words. fourth order parabolic equation, existence, asymptotic behavior.

This work is supported by the Tianyuan Fund for Mathematics of P.R. China (No. 10526022).