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- W4382601434 abstract "In Chapter 25, we linked minimizers of a functional to the stationary solution of a PDE. A crucial ingredient has been convexity. In this chapter, we are going to study a nonconvex functional in combination with a tool similar to the Intermediate Value Theorem to obtain nontrivial time-periodic solutions. We want to study the cubic nonlinear wave equationfor u = u(x, t) and x ∈ (0, π). The goal is to prove the following result:Theorem 26.1. (time-periodic waves) There exists a nontrivial (u ≠ 0 on a set of positive Lebesgue measure) and 2π-time-periodic solution to (26.1)." @default.
- W4382601434 created "2023-06-30" @default.
- W4382601434 date "2019-01-01" @default.
- W4382601434 modified "2023-09-24" @default.
- W4382601434 title "Chapter 26: Mountain Passes and Periodic Waves" @default.
- W4382601434 doi "https://doi.org/10.1137/1.9781611975666.ch26" @default.
- W4382601434 hasPublicationYear "2019" @default.
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