Generalized ergodic problems: existence and uniqueness structures of solutions
| Autor: | Hiroyoshi Mitake, Wenjia Jing, Hung V. Tran |
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| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Regular polygon Contact type Torus 35B10 35B27 35B40 35D40 35F21 49L25 01 natural sciences 010101 applied mathematics Nonlinear system Mathematics - Analysis of PDEs FOS: Mathematics Ergodic theory Uniqueness 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics |
| Popis: | We study a generalized ergodic problem (E), which is a Hamilton-Jacobi equation of contact type, in the flat $n$-dimensional torus. We first obtain existence of solutions to this problem under quite general assumptions. Various examples are presented and analyzed to show that (E) does not have unique solutions in general. We then study uniqueness structures of solutions to (E) in the convex setting by using the nonlinear adjoint method. 21 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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