$L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$

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

L^{p}

-estimates for hyperbolic operators applications to

□ u = u^{k}

Peral, I.¹ ; Peral, J. C.¹ ; Walias, M.¹

¹ Facultad de Ciencias, Division de Matematicas C-XVI, Universidad Autonoma de Madrid. Cantoblanco, Madrid-34 - Spain.

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 5, Tome 4 (1982) no. 2, pp. 143-152.

Zbl

Affiliations des auteurs :

Peral, I. ¹ ; Peral, J. C. ¹ ; Walias, M. ¹

¹ Facultad de Ciencias, Division de Matematicas C-XVI, Universidad Autonoma de Madrid. Cantoblanco, Madrid-34 - Spain.

@article{AFST_1982_5_4_2_143_0,
     author = {Peral, I. and Peral, J. C. and Walias, M.},
     title = {$L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {143--152},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 5, 4},
     number = {2},
     year = {1982},
     zbl = {0508.35053},
     language = {en},
     url = {http://archive.numdam.org/item/AFST_1982_5_4_2_143_0/}
}

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Peral, I.; Peral, J. C.; Walias, M. $L^p$-estimates for hyperbolic operators applications to $\Box u = u^k$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 5, Tome 4 (1982) no. 2, pp. 143-152. http://archive.numdam.org/item/AFST_1982_5_4_2_143_0/

Bibliographie
Cité par

[1] W. Littman. «The wave operator and Lp norms». J. Math. Mech.12 (1963) 55-68. | MR | Zbl

[2] W. Littman. «Multipliers in Lp and interpolation». Bull. A.M.S. 71 (1965) 764-766. | MR | Zbl

[3] J.C. Peral. «Lp-estimates for wave equations». Journal of Functional Analysis, Vol 36, n° 1 (1980), 114-145. | MR | Zbl

[4] I. Segal. «Non-linear semi-groups». Annals in Mathematics 78 n° 2 (1963) 339-364. | MR | Zbl

[5] I. Segal. «The global Cauchy Problem for a realtivistic scalar field with power interaction». Bull. Soc. Math. France 91 (1963) 129-135. | Numdam | MR | Zbl

[6] W. Strauss. «Non-linear invariant wave equations». Lecture notes in Phisics n° 73, Springer-Verlag, Berlin (1978).

[7] W. Strauss, L. Vazquez. «Numerical solution of a Non-linear Klein-Gordon Equations». J. Comp. Phys. 28 n°2 (1978) 271-278. | MR | Zbl

[8] R.S. Strichartz. «Convolutions with Kernels having singularities on a sphere». Trans. Amer. Math. Soc. 148 (1970) 461-471. | MR | Zbl

[9] R.S. Strichartz. «A priori Estimates for the Wave Equations and some applications». Jour. Functional Analysis 5 (1970) 218-235. | MR | Zbl