Ray and Explosive Solutions of Nonlinear Evolutional Equations in Hilbert Space.
CALIFORNIA UNIV LOS ANGELES SCHOOL OF ENGINEERING AND APPLIED SCIENCE
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Many nonlinear phenomena occurring in physical systems are describable by a set of ordinary, partial or functional differential equations which can be regarded as an evolutional equation in a suitable abstract vector space. In this paper, the author considers nonlinear evolutional equations defined on Hilbert spaces. Attention is focused on developing conditions for the existence of solutions which lie along half-rays emanating from the origin of the space. The results are used to establish sufficient conditions for the existence or nonexistence of explosive solutions or solutions having finite escape time. The paper concludes with a discussion of the application of some of the results to specific classes of evolutional equations arising from physical situations. Author
- Theoretical Mathematics
- Plasma Physics and Magnetohydrodynamics