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The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces

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Publication:1904213
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DOI10.1016/S0294-1449(16)30179-2zbMath0836.34064OpenAlexW2498581938MaRDI QIDQ1904213

Piero D'Ancona

Publication date: 22 April 1996

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1994__11_4_343_0


zbMATH Keywords

degenerate hyperbolic equationsabstract nonlinear second order equationOlejnik's conditions


Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Nonlinear differential equations in abstract spaces (34G20) Second-order nonlinear hyperbolic equations (35L70)


Related Items

Oscillatory properties for semilinear degenerate hyperbolic equations of second order



Cites Work

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  • An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
  • Global existence for abstract evolution equations of weakly hyperbolic type
  • Remarks on evolution inequalities
  • An abstract form of the nonlinear Cauchy-Kowalewski theorem
  • Remarks on the abstract form of nonlinear cauchy-kovalevsky theorems
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