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Errata: Regular solutions of wave equations with super-critical sources and exponential-to-logarithmic damping

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  • This note is an errata for the paper [2] which discusses regular solutions to wave equations with super-critical source terms. The purpose of this note is to address the gap in the proof of uniqueness of such solutions.
    Mathematics Subject Classification: Primary: 35L05; Secondary: 35A01, 35L20, 35B33, 46E30.

    Citation:

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  • [1]

    R. A. Adams and J. J. F. Fournier, Sobolev Spaces, Second edition, Pure and Applied Mathematics (Amsterdam), 140, Elsevier/Academic Press, Amsterdam, 2003.

    [2]

    L. Bociu, P. Radu and D. Toundykov, Regular solutions of wave equations with super-critical sources and exponential-to-logarithmic damping, Evolution Equations and Control Theory, 2 (2013), 255-279.doi: 10.3934/eect.2013.2.255.

    [3]

    T. K. Donaldson and N. S. Trudinger, Orlicz-Sobolev spaces and imbedding theorems, J. Functional Analysis, 8 (1971), 52-75.doi: 10.1016/0022-1236(71)90018-8.

    [4]

    H. Hudzik, Intersections and algebraic sums of Musielak-Orlicz spaces, Portugal. Math., 40 (1981), 287-296 (1985).

    [5]

    M. A. Krasnosel$'$skiĭ and Ja. B. Rutickiĭ, Convex Functions and Orlicz Spaces, Translated from the first Russian edition by Leo F. Boron. P. Noordhoff Ltd., Groningen, 1961.

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