Timeline for On bounded solutions of a given fourth-order linear ODE
Current License: CC BY-SA 4.0
6 events
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| Oct 23, 2022 at 18:53 | comment | added | Milen Ivanov | @PiyushGrover I know about spatial dynamics, this is where this problem came up from! I have an ODE coming from a hyperbolic PDE and I was trying to prove that the stable and unstable manifolds intersect transversely. Unfortunately, to apply Evans Function theory, I have to cast the ODE as a system (easy) and find a solution $\psi$ of the adjoint ODE, which I was unable to do. If I had $psi$ I would have looked at something like $M:=\int \phi'(x) \dot \psi(x) dx$ (the derivative of the Evans function at zero), and tried to prove $M\neq 0$. However, this falls apart without $\psi$. | |
| Oct 22, 2022 at 23:44 | comment | added | Piyush Grover | The methods you need come from "spatial dynamics". Look up Evans function, e.g. in this book: Kapitula, Todd, and Keith Promislow. Spectral and dynamical stability of nonlinear waves. Vol. 457. New York: Springer, 2013. Another keyword: exponential dichotomy | |
| Oct 21, 2022 at 9:52 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing
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| Oct 21, 2022 at 8:37 | history | edited | Milen Ivanov | CC BY-SA 4.0 |
added 2 characters in body
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| S Oct 21, 2022 at 8:16 | review | First questions | |||
| Oct 21, 2022 at 8:26 | |||||
| S Oct 21, 2022 at 8:16 | history | asked | Milen Ivanov | CC BY-SA 4.0 |