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Global version of the Cauchy-Kovalevskaia theorem for nonlinear PDEs

✍ Scribed by Elemer E. Rosinger


Publisher
Springer Netherlands
Year
1990
Tongue
English
Weight
515 KB
Volume
21
Category
Article
ISSN
0167-8019

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✦ Synopsis


The existence of global generalized solutions is proved for arbitrary analytic nonlinear PDEs on the whole of their domains of analyticity. The solutions are analytic outside of closed, nowhere dense subsets.


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The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is