Jung, Soon-Mo On the stability of wave equation. (English) Zbl 1470.39065 Abstr. Appl. Anal. 2013, Article ID 910565, 6 p. (2013). Summary: We prove the generalized Hyers-Ulam stability of the wave equation, \(\Delta u = (1 / c^2) u_{t t}\), in a class of twice continuously differentiable functions under some conditions. MSC: 39B82 Stability, separation, extension, and related topics for functional equations PDF BibTeX XML Cite \textit{S.-M. Jung}, Abstr. Appl. Anal. 2013, Article ID 910565, 6 p. (2013; Zbl 1470.39065) Full Text: DOI References: [1] Ulam, S. M., A Collection of Mathematical Problems (1960), New York, NY, USA: Interscience, New York, NY, USA · Zbl 0086.24101 [2] Hyers, D. H., On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America, 27, 222-224 (1941) · Zbl 0061.26403 [3] Rassias, T. M., On the stability of the linear mapping in Banach spaces, Proceedings of the American Mathematical Society, 72, 2, 297-300 (1978) · Zbl 0398.47040 [4] Brillouët-Belluot, N.; Brzdęk, J.; Ciepliński, K., On some recent developments in Ulam’s type stability, Abstract and Applied Analysis, 2012 (2012) · Zbl 1259.39019 [5] Forti, G. L., Hyers-Ulam stability of functional equations in several variables, Aequationes Mathematicae, 50, 1-2, 143-190 (1995) · Zbl 0836.39007 [6] Găvruţa, P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, Journal of Mathematical Analysis and Applications, 184, 3, 431-436 (1994) · Zbl 0818.46043 [7] Hyers, D. H.; Isac, G.; Rassias, T. M., Stability of Functional Equations in Several Variables (1998), Boston, Mass, USA: Birkhäauser, Boston, Mass, USA · Zbl 0907.39025 [8] Hyers, D. H.; Rassias, T. M., Approximate homomorphisms, Aequationes Mathematicae, 44, 2-3, 125-153 (1992) · Zbl 0806.47056 [9] Jung, S.-M., Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, 48 (2011), New York, NY, USA: Springer, New York, NY, USA · Zbl 1221.39038 [10] Rassias, T. M., On the stability of functional equations and a problem of Ulam, Acta Applicandae Mathematicae, 62, 1, 23-130 (2000) · Zbl 0981.39014 [11] Evans, L. C., Partial Differential Equations, 19 (1998), Providence, RI, USA: American Mathematical Society, Providence, RI, USA [12] Hegyi, B.; Jung, S.-M., On the stability of Laplace’s equation, Applied Mathematics Letters, 26, 5, 549-552 (2013) · Zbl 1266.35014 [13] Jung, S.-M., Hyers-Ulam stability of linear differential equations of first order. II, Applied Mathematics Letters, 19, 9, 854-858 (2006) · Zbl 1125.34328 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.