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Struwe, Michael

Semilinear wave equations. (English) Zbl 0767.35045

Bull. Am. Math. Soc., New Ser. 26, No. 1, 53-85 (1992).
Summary: We survey existence and regularity results for semi-linear wave equations. In particular, we review the recent regularity results for the \(u^ 5\)-Klein-Gordon equation by M. G. Grillakis [Ann. Math., II. Ser. 132, No. 3, 485-509 (1990; Zbl 0736.35067)] and this author [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV, Ser. 15, No. 3, 495-513 (1988; Zbl 0728.35072)] and give a self-contained, slightly simplified proof.

Cited in 34 Documents

MSC:

35L70 Second-order nonlinear hyperbolic equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35L05 Wave equation
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35Q40 PDEs in connection with quantum mechanics

Keywords:

initial value problems; Klein-Gordon equation; existence; regularity

Citations:

Zbl 0736.35067; Zbl 0728.35072
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\textit{M. Struwe}, Bull. Am. Math. Soc., New Ser. 26, No. 1, 53--85 (1992; Zbl 0767.35045)
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References:

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