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Levine, H.A. (1974) Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the form Pu = -Au + F(u). Transactions of the American Mathematical Society, 192, 1-21.
https://doi.org/10.1090/S0002-9947-1974-0344697-2

has been cited by the following article:

• TITLE: The Quality Properties of Integral Type Problems for Wave Equations and Applications

  AUTHORS: Veli B. Shakhmurov, Rishad Shahmurov

  KEYWORDS: Abstract Differential Equations, Boussinesq Equations, Wave Equations, Regularity Property of Solutions, Fourier Multipliers

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.4, April 21, 2022

  ABSTRACT: In this paper, the integral problem for linear and nonlinear wave equations is studied. The equation involves abstract operator A in Hilbert space H. Here, assuming enough smoothness on the initial data and the operators, the existence, uniqueness, regularity properties of solutions are established. By choosing the space H and A, the regularity properties of solutions of a wide class of wave equations in the field of physics are obtained.