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

Lorena Bociu; Petronela Radu; Daniel Toundykov

doi:10.3934/eect.2014.3.349

Article Contents

2014, Volume 3, Issue 2: 349-354. Doi: 10.3934/eect.2014.3.349

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

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: June 2014

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Abstract

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:

Mathematics Subject Classification: Primary: 35L05; Secondary: 35A01, 35L20, 35B33, 46E30.

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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.