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Proceedings of the American Mathematical Society

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Higher order estimates and smoothness of nonlinear wave equations

Author: Michael C. Reed
Journal: Proc. Amer. Math. Soc. 51 (1975), 79-85
MSC: Primary 35L60; Secondary 47D05, 47H15
MathSciNet review: 0377238
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Abstract: A completely elementary proof is given for Segal's nonlinear semigroup theorem.

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  • [1] J. Chadam, Asymptotics for $ \square u = {m^2} + G(x,t,u,{u_x},{u_t})$. I and II: Global existence and decay, Ann. Scuola Norm. Sup. Pisa 26 (1972), 33-65, 67-95.
  • [2] John M. Chadam, Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac equations in one space dimension, J. Functional Analysis 13 (1973), 173–184. MR 0368640
  • [3] J. B. Keller, On solutions of nonlinear wave equations, Comm. Pure Appl. Math. 10 (1957), 523–530. MR 0096889
  • [4] Walter Littman, The wave operator and 𝐿_{𝑝} norms, J. Math. Mech. 12 (1963), 55–68. MR 0146521
  • [5] Michael Reed and Barry Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0493420
  • [6] Irving Segal, Non-linear semi-groups, Ann. of Math. (2) 78 (1963), 339–364. MR 0152908
  • [7] Walter Alexander Strauss, The energy method in nonlinear partial differential equations, Notas de Matemática, No. 47, Instituto de Matemática Pura e Aplicada, Conselho Nacional de Pesquisas, Rio de Janeiro, 1969. MR 0273170

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Keywords: Nonlinear, wave equation, semigroup
Article copyright: © Copyright 1975 American Mathematical Society