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A non-linear hyperbolic equation

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  • Eliana Henriques de Brito

Abstract

In this paper the following Cauchy problem, in a Hilbert space H , is considered: ( I + λ A ) u ″ + A 2 u + [ α + M ( | A 1 2 u | 2 ) ] A u = f u ( 0 ) = u 0 u ′ ( 0 ) = u 1 M and f are given functions, A an operator in H , satisfying convenient hypothesis, λ ≥ 0 and α is a real number. For u 0 in the domain of A and u 1 in the domain of A 1 2 , if λ > 0 , and u 1 in H , when λ = 0 , a theorem of existence and uniqueness of weak solution is proved.

Suggested Citation

  • Eliana Henriques de Brito, 1980. "A non-linear hyperbolic equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 3, pages 1-16, January.
    • Handle: RePEc:hin:jijmms:732105
    DOI: 10.1155/S0161171280000385
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