A semilinear curl-curl problem in \(\mathbb{R}^3\)
Institución: Stockholm University
Tipo de Evento: Investigación
Cuándo |
23/10/2018 de 11:00 a 12:00 |
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Dónde | Salón de seminarios "Graciela Salicrup" |
Agregar evento al calendario |
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Abstract.
We look for nontrivial solutions to the system of semilinear equations
(*) $$\nabla\times\nabla\times E = f(x,E) \text{ in } \mathbb{R}^3,$$
where $E: \mathbb{R}^3\to\mathbb{R}^3$ and $f=\nabla_EF$. This system arises when looking for time-periodic solutions to Maxwell equations with nonlinear polarization.
The main difficulties here are due to unboundedness of the domain and infinite dimension of the kernel of the left-hand side of (*).
We first discuss an abstract result for a class of functionals related to this problem and then apply it to prove the existence of a ground state solution as well as infinitely many geometrically distinct solutions to (*) for some classes of $f$.
This talk is based on a work in progress with J. Mederski and J. Schino.