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Logarithmic convexity and the Cauchy problem for P(t)utt+M(t)ut+N(t)u=C in Hilbert space

  • Howard A. Levine
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 316)

Keywords

Cauchy Problem Operator Family Symmetric Part Continuous Dependence Unique Continuation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

  1. [1]
    S. Agmon, Unicité et convexité dans les problèmes différentiels, Sem. Math. Sup. (1965), Univ. of Montreal Press (1966).Google Scholar
  2. [2]
    S. Agmon and L. Nirenberg, Lower bounds and uniqueness theorems for solutions of differential equations in a Hilbert space, Comm. Pure Appl. Math. 20 (1967) 207–229.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, Inc. (1969).zbMATHGoogle Scholar
  4. [4]
    F. John, Continuous dependence on data for solutions of partial differential equations with a prescribed bound, Comm. Pure Appl. Math. 13 (1960) 551–585.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    R.J. Knops and L.E. Payne, Stability in linear elasticity, Int. Journal of Solid Structures 4 (1968) 1233–1242.CrossRefzbMATHGoogle Scholar
  6. [6]
    R.J. Knops and L.E. Payne, On uniqueness and continuous dependence in dynamical problems of linear thermoelasticity, Int. Journal of Solid Structures 6 (1970) 1173–1184.CrossRefzbMATHGoogle Scholar
  7. [7]
    Y.Y. Kim, On the spectrum of an operator connected with a mixed problem, Differentrial'nye Uravneniya 3 (1967) 109–113.MathSciNetGoogle Scholar
  8. [8]
    H.A. Levine, On a theorem of Knops and Payne in dynamical linear thermoelasticity, Arch. Rat. Mech. Anal. 38 (1970) 290–307.CrossRefzbMATHGoogle Scholar
  9. [9]
    H.A. Levine, Logarithmic convexity, first order differential inequalities and some applications, Trans. Am. Math. Soc. 152 (1970) 299–320.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    H.A. Levine, Logarithmic convexity and the Cauchy problem for some abstract second order differential inequalities, J. Differential Equations 8 (1970), 34–55.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    J.L. Lions, Equations Différentiel es et Opérationelles et Problèmes aux Limites, Springer Verlag (1961).Google Scholar
  12. [12]
    L.E. Payne, Bounds in the Cauchy problem for the Laplace equation, Arch. Rat. Mech. Anal. 5 (1960) 35–45.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    L.E. Payne, On some nonwell posed problems for partial differential equations, Proc. Adv. Sympos. Numerical Solutions of Nonlinear Differential Equations (Madison Wisc. 1966) Wiley, N.Y. (1966) 239–263.Google Scholar
  14. [14]
    L.E. Payne and D. Sather, On some improperly posed problems for quasilinear equations of mixed type, Trans. Amer. Math. Soc. 128 (1967) 135–141.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    F. Riesz and B. Sz.-Nagy, Functional Analysis, Ungar Pub. Co. (1961).Google Scholar
  16. [16]
    S.L. Sobolev, 48 Reunione Socièta Italiana per il progresso della Scienza, Roma (1965) 192–208.Google Scholar
  17. [17]
    T.S. Zelenjak, A mixed problem for an equation which cannot be solved for the highest order time deviative, DAN, SSSR (6) (1965) 1225–1228.Google Scholar

Copyright information

© Springer-Verlag Berlin 1973

Authors and Affiliations

  • Howard A. Levine
    • 1
  1. 1.School of Mathematics, Institute of TechnologyUniversity of MinnesotaMinneapolis

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