L p -estimates for hyperbolic operators applications to □ u = u k

I. Peral; J. C. Peral; M. Walias

Annales de la Faculté des sciences de Toulouse : Mathématiques (1982)

  • Volume: 4, Issue: 2, page 143-152
  • ISSN: 0240-2963

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Peral, I., Peral, J. C., and Walias, M.. "$L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$." Annales de la Faculté des sciences de Toulouse : Mathématiques 4.2 (1982): 143-152. <http://eudml.org/doc/73132>.

@article{Peral1982,
author = {Peral, I., Peral, J. C., Walias, M.},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {non-homogeneous wave equation; existence and uniqueness of weak solutions},
language = {eng},
number = {2},
pages = {143-152},
publisher = {UNIVERSITE PAUL SABATIER},
title = {$L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$},
url = {http://eudml.org/doc/73132},
volume = {4},
year = {1982},
}

TY - JOUR
AU - Peral, I.
AU - Peral, J. C.
AU - Walias, M.
TI - $L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 1982
PB - UNIVERSITE PAUL SABATIER
VL - 4
IS - 2
SP - 143
EP - 152
LA - eng
KW - non-homogeneous wave equation; existence and uniqueness of weak solutions
UR - http://eudml.org/doc/73132
ER -

References

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  1. [1] W. Littman. «The wave operator and Lp norms». J. Math. Mech.12 (1963) 55-68. Zbl0127.31705MR146521
  2. [2] W. Littman. «Multipliers in Lp and interpolation». Bull. A.M.S.71 (1965) 764-766. Zbl0156.36504MR179544
  3. [3] J.C. Peral. «Lp-estimates for wave equations». Journal of Functional Analysis, Vol 36, n° 1 (1980), 114-145. Zbl0442.35017MR568979
  4. [4] I. Segal. «Non-linear semi-groups». Annals in Mathematics78 n° 2 (1963) 339-364. Zbl0204.16004MR152908
  5. [5] I. Segal. «The global Cauchy Problem for a realtivistic scalar field with power interaction». Bull. Soc. Math. France91 (1963) 129-135. Zbl0178.45403MR153967
  6. [6] W. Strauss. «Non-linear invariant wave equations». Lecture notes in Phisics n° 73, Springer-Verlag, Berlin (1978). 
  7. [7] W. Strauss, L. Vazquez. «Numerical solution of a Non-linear Klein-Gordon Equations». J. Comp. Phys.28 n°2 (1978) 271-278. Zbl0387.65076MR503140
  8. [8] R.S. Strichartz. «Convolutions with Kernels having singularities on a sphere». Trans. Amer. Math. Soc.148 (1970) 461-471. Zbl0199.17502MR256219
  9. [9] R.S. Strichartz. «A priori Estimates for the Wave Equations and some applications». Jour. Functional Analysis5 (1970) 218-235. Zbl0189.40701MR257581

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