Abstract
This chapter discusses nonlinear oscillations under hyperbolic systems. It presents hyperbolic systems of first-order partial differential equations in the canonic forms of Courant-Lax and of Schauder. For these systems in a slab Da = [0 ≥ x ≥ a, y ɛ Er] of the xy-space Er+1, the chapter presents the formulation of certain boundary value problems, and presents the corresponding theorems of existence of the solutions, and of their uniqueness and continuous dependence on the data. In particular, if all the data are periodic of given periods in the y-coordinates, then the solutions are also periodic of the same periods. Theorems A and B presented in the chapter contain a specific hypothesis, which can be briefly stated by saying that the relevant matrices have “dominant main diagonal”. By an example, the chapter presents that the conclusions of the same theorems may not hold if such specific condition is not satisfied.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
