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

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June 2014, 3(2): 349-354. doi: 10.3934/eect.2014.3.349

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

Lorena Bociu ^1, , Petronela Radu ^2, and Daniel Toundykov ^3,

1.	Department of Mathematics, NC State University, Raleigh, NC 27695
2.	Department of Mathematics, University of Nebraska-Lincoln, Avery Hall 239, Lincoln, NE 68588
3.	Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588

Received September 2013 Revised February 2014 Published May 2014

Abstract
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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.

Keywords: nonlinear damping., super-critical, critical exponent, regular solutions, Wave equation.

Mathematics Subject Classification: Primary: 35L05; Secondary: 35A01, 35L20, 35B33, 46E3.

Citation: Lorena Bociu, Petronela Radu, Daniel Toundykov. Errata: Regular solutions of wave equations with super-critical sources and exponential-to-logarithmic damping. Evolution Equations and Control Theory, 2014, 3 (2) : 349-354. doi: 10.3934/eect.2014.3.349

References:

[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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References:

[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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