A uniqueness theorem for statistical solutions of a certain non-linear hyperbolic equation

1983 ◽  
Vol 38 (6) ◽  
pp. 129-130
Author(s):  
S I Sobolev
Keyword(s):  
Hyperbolic Equation ◽  
Uniqueness Theorem ◽  
Linear Hyperbolic Equation ◽  
Non Linear ◽  
Statistical Solutions

scholarly journals A non-linear hyperbolic equation

1980 ◽  
Vol 3 (3) ◽  
pp. 505-520 ◽  
Author(s):  
Eliana Henriques de Brito
Keyword(s):  
Hilbert Space ◽  
Cauchy Problem ◽  
Weak Solution ◽  
Real Number ◽  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Linear Hyperbolic Equation ◽  
Non Linear

In this paper the following Cauchy problem, in a Hilbert spaceH, is considered:(I+λA)u″+A2u+[α+M(|A12u|2)]Au=fu(0)=u0u′(0)=u1Mandfare given functions,Aan operator inH, satisfying convenient hypothesis,λ≥0andαis a real number.Foru0in the domain ofAandu1in the domain ofA12, ifλ>0, andu1inH, whenλ=0, a theorem of existence and uniqueness of weak solution is proved.

Oscillation of second-order hyperbolic equations with non-integrable coefficients

1982 ◽  
Vol 91 (3-4) ◽  
pp. 305-313 ◽  
Author(s):  
Wu-Teh Hsiang ◽  
Man Kam Kwong
Keyword(s):  
Hyperbolic Equation ◽  
Hyperbolic Equations ◽  
Sufficient Conditions ◽  
Second Order ◽  
Linear Case ◽  
Linear Hyperbolic Equation ◽  
Initial Values ◽  
Non Linear ◽  
Image Position

SynopsisSome sufficient conditions are obtained on the coefficient g and the initial values Φ and ψfor the solution ot the non-linear hyperbolic equationto change sign in the first quadrant. An example is given to show that is not sufficient in the linear case.

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