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ON A PERTURBED CONSERVATIVE SYSTEM OF SEMILINEAR WAVE EQUATIONS WITH PERIODIC-DIRICHLET BOUNDARY CONDITIONS
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JINHAI CHEN, DONAL O’REGAN
Journal:

Bulletin of the Australian Mathematical Society / Volume 81 / Issue 2 / April 2010

Published online by Cambridge University Press:

13 January 2010, pp. 281-288

Print publication:

April 2010
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In this paper, some existence and uniqueness results for generalized solutions to a periodic-Dirichlet problem for semilinear wave equations are given, using a global inverse function theorem. These results extend those known in the literature.

Boundedness of Solutions of Parabolic Equations With Anisotropic Growth Conditions
Yu Mingqi, Lian Xiting
Journal:

Canadian Journal of Mathematics / Volume 49 / Issue 4 / 01 August 1997

Published online by Cambridge University Press:

20 November 2018, pp. 798-809

Print publication:

01 August 1997
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In this paper, we consider the parabolic equation with anisotropic growth conditions, and obtain some criteria on boundedness of solutions, which generalize the corresponding results for the isotropic case.