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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

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 & 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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

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

[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. Google Scholar

show all references

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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[4]

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

[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. Google Scholar

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