Existence of Solutions for a Semilinear Wave Equation With Non-Monotone Nonlinearity

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Benjamin Preskill '09, Harvey Mudd CollegeFollow

Student Co-author

HMC Undergraduate

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

10-2010

Abstract

For double-periodic and Dirichlet-periodic boundary conditions, we prove the existence of solutions to a forced semilinear wave equation with asymptotically linear nonlinearity, no resonance, and non-monotone nonlinearity when the forcing term is not flat on characteristics. The solutions are in L^∞ when the forcing term is in L^∞ and continous when the forcing term is continuous. This is in contrast with the results in [4], where the non-enxistence of continuous solutions is established even when forcing term is of class C^∞ but is flat on a characteristic.

Comments

Author's post-print manuscript is posted.

The published article can be found at http://dx.doi.org/10.3934/dcds.2010.28.649

Rights Information

© 2010 American Institute of Mathematical Sciences

DOI

10.3934/dcds.2010.28.649

Recommended Citation

Castro, Alfonso and Benjamin Preskill. “Existence of solutions for a semilinear wave equation with non-monotone nonlinearity”, Continuous and Discrete Dynamical Systems, Series A, Vol. 28, No. 2, (2010), pp. 649-658.