Abstract
Selfdual variational calculus is developed further and used to address questions of existence of local and global solutions for various parabolic semi-linear equations, and Hamiltonian systems of PDEs. This allows for the resolution of such equations under general time boundary conditions which include the more traditional ones such as initial value problems, periodic and anti-periodic orbits, but also yield new ones such as “periodic orbits up to an isometry” for evolution equations that may not have periodic solutions. In the process, we introduce a method for perturbing selfdual functionals in order to induce coercivity and compactness, without destroying the selfdual character of the system.
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N. Ghoussoub was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada. A. Moameni’s research was supported by a postdoctoral fellowship at the University of British Columbia.
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Ghoussoub, N., Moameni, A. Hamiltonian systems of PDEs with selfdual boundary conditions. Calc. Var. 36, 85–118 (2009). https://doi.org/10.1007/s00526-009-0224-7
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DOI: https://doi.org/10.1007/s00526-009-0224-7