Pacific Journal of Mathematics

Maximum and monotonicity properties of initial boundary value problems for hyperbolic equations.

D. Sather

Article information

Source
Pacific J. Math., Volume 19, Number 1 (1966), 141-157.

Dates
First available in Project Euclid: 13 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102993961

Mathematical Reviews number (MathSciNet)
MR0208158

Zentralblatt MATH identifier
0144.34804

Subjects
Primary: 35.55

Citation

Sather, D. Maximum and monotonicity properties of initial boundary value problems for hyperbolic equations. Pacific J. Math. 19 (1966), no. 1, 141--157. https://projecteuclid.org/euclid.pjm/1102993961


Export citation

References

  • [1] S. Agmon, L. Nirenberg and M. H. Protter, A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type, Comm. Pure Appl. Math. 6 (1953), 455-470.
  • [2] P. Garabedian, Partial DifferentialEquations, John Wiley and Sons, New York, 1964.
  • [3] P. Germain and R. Bader, Sur le prbleme de Tricomi, Rend. Circ. Mat. Palermo 2 (1953), 53.
  • [4] H. Gloistehn, Monotoniesdtze und Fehlerabschatzungen fur Anfangswertaufgabenmit hyperbolischer Differentialgleichung, Arch. Rational Mech. Anal. 14 (1963), 384-404.
  • [5] J. Hadamard, Sur un probleme mixte aux derivees partielles, Bull. Soc. Math. France 31 (1903), 208-224.
  • [6] J. Hadamard, Resolution d'un probleme aux limites pour les equations lineaires du type hyperbolique, Bull. Soc. Math. France 32 (1904), 242-268.
  • [7] M. H. Protter, A maximum principle for hyperbolic equations in a neighborhoodof an initial line, Trans. Amer. Math. Soc. 87 (1958), 119-129.
  • [8] D. Sather, Maximum properties of Cauchy's problem in three-dimensional space- time, Arch. Rational Mech. Anal. 18 (1965), 14-26.
  • [9] D. Sather, A maximum property of Cauchy's problem in n-dimensionalspace-time, Arch. Rational Mech. Anal. 18 (1965), 27-38.
  • [10] D. Sather, A maximum property of Cauchy's problem for the wave operator, Arch. Rational Mech. Anal. 21 (1966), 303-309.
  • [11] G. N. Watson, Theory of Bessel Functions, Cambridge, 1944.
  • [12] H. F. Weinberger, A maximum property of Cauchy's problem, Ann. of Math. 64 (1956), 505-513.
  • [13] H. F. Weinberger, A maximum property of Cauchy's problem in three-dimensional space- time, Proceedings of Symposia in Pure Mathematics, Vol. IV, Partial Differential Equations, American Mathematical Society, 1961, 91-99.
  • [14] A. Weinstein, On a Cauchy problem with subharmonic initialvalues, Ann. Mat. Pura Appl. 43 (1957), 325-340.
  • [15] A. Weinstein, Hyperbolic and parabolic equations with subharmonic data, Symposium on the Numerical Treatment of Partial Differential Equations with Real Characteristics, Prov. Intern. Computation Centre, Rome, 1959, 74-86.