- 期刊
A NON-LINEAR HYPERBOLIC EQUATION
並列摘要
In this paper the following Cauchy problem, in a Hilbert space H, is considered: (I+λA)u＂+A^2u+[α+M(|A^(1/2)u|^2)]Au=f u(0)=u_0 u'(0)=u_1 M and f are given functions, A an operator in H, satisfying convenient hypothesis, λ≥0 and α is a real number. For u_0 in the domain of A and u_1 in the domain of A^(1/2), if λ＞0, and u_1 in H, when λ=0, a theorem of existence and uniqueness of weak solution is proved.
延伸閱讀
- MESLOUB, S., & BOUZIANI, A. (1999). ON A CLASS OF SINGULAR HYPERBOLIC EQUATION WITH A WEIGHTED INTEGRAL CONDITION. International Journal of Mathematics and Mathematical Sciences, 1999(), 511-519. https://doi.org/10.1155/S0161171299225112
- Gadjiev, T., Rasulov, R., & Aliev, O. (2012). On Behavior of Solution of Degenerated Hyperbolic Equation. ISRN Applied Mathematics, (), 373-382. https://doi.org/10.5402/2012/124936
- Domoshnitsky, A., Lomtatidze, A., Maghakyan, A., & □remr, J. (2011). Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side. Abstract and Applied Analysis, (2011), 671-696. https://doi.org/10.1155/2011/242965
- EBIHARA, Y., & PEREIRA, D. (1989). ON A GLOBAL CLASSICAL SOLUTION OF A QUASILINEAR HYPERBOLIC EQUATION. International Journal of Mathematics and Mathematical Sciences, 1989(), 29-37. https://doi.org/10.1155/S0161171289000049
- BOUZIANI, A. (2004). A MIXED PROBLEM WITH ONLY INTEGRAL BOUNDARY CONDITIONS FOR A HYPERBOLIC EQUATION. International Journal of Mathematics and Mathematical Sciences, 2004(), 1279-1291-087. https://doi.org/10.1155/S0161171204204240