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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, (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.  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.  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.   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., (1961).   Google Scholar

show all references

References:
[1]

R. A. Adams and J. J. F. Fournier, Sobolev Spaces,, Second edition, (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.  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.  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.   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., (1961).   Google Scholar

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