GLOBAL EXISTENCE FOR A CLASS OF SYSTEMS OF NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS-中国期刊网

摘要 Considerasystemofnonlinearwaveequations(e)2t-c2i△xui=Fi(u,(e)u,(e)x(e)u)in(0,∞)×(R)3fori=1,┈,m,whereFi(i=1,┈,m)aresmoothfunctionsofdegree2neartheoriginoftheirarguments,andu=(u1,┈,um),while(e)uand(e)x(e)urepresentthefirstand(secondderivativesofu,respectively.Inthispaper,theauthorpresentsanewclassofnonlinearityforwhichtheglobalexistenceofsmallsolutionsisensured.Forexample,globalexistenceofsmallsolutionsfor((e)2t-c21Δx)u1=u2((e)tu2)+arbitrarycubicterms,((e)2t-c22Δx)u2=u1((e)tu2)+((e)tu1)u2+arbitrarycubictermswillbeestablished,providedthatc21≠c22.

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GLOBAL EXISTENCE FOR A CLASS OF SYSTEMS OF NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

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GLOBAL EXISTENCE FOR A CLASS OF SYSTEMS OF NONLINEAR WAVE EQUATIONS IN THREE SPACE DIMENSIONS

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