American Institute of Mathematical Sciences

Advanced
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

[1]

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

Tomasz Dlotko, Tongtong Liang, Yejuan Wang. Critical and super-critical abstract parabolic equations. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1517-1541. doi: 10.3934/dcdsb.2019238
[3]

Igor Chueshov, Irena Lasiecka, Daniel Toundykov. Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent. Discrete & Continuous Dynamical Systems - A, 2008, 20 (3) : 459-509. doi: 10.3934/dcds.2008.20.459
[4]

Jiayun Lin, Kenji Nishihara, Jian Zhai. Critical exponent for the semilinear wave equation with time-dependent damping. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4307-4320. doi: 10.3934/dcds.2012.32.4307
[5]

A. M. Micheletti, Monica Musso, A. Pistoia. Super-position of spikes for a slightly super-critical elliptic equation in $R^N$. Discrete & Continuous Dynamical Systems - A, 2005, 12 (4) : 747-760. doi: 10.3934/dcds.2005.12.747
[6]

Sergey Zelik. Asymptotic regularity of solutions of a nonautonomous damped wave equation with a critical growth exponent. Communications on Pure & Applied Analysis, 2004, 3 (4) : 921-934. doi: 10.3934/cpaa.2004.3.921
[7]

A. Kh. Khanmamedov. Global attractors for strongly damped wave equations with displacement dependent damping and nonlinear source term of critical exponent. Discrete & Continuous Dynamical Systems - A, 2011, 31 (1) : 119-138. doi: 10.3934/dcds.2011.31.119
[8]

Maurizio Grasselli, Vittorino Pata. On the damped semilinear wave equation with critical exponent. Conference Publications, 2003, 2003 (Special) : 351-358. doi: 10.3934/proc.2003.2003.351
[9]

Masahiro Ikeda, Takahisa Inui, Mamoru Okamoto, Yuta Wakasugi. $ L^p $-$ L^q $ estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1967-2008. doi: 10.3934/cpaa.2019090
[10]

Mohamad Darwich. On the $L^2$-critical nonlinear Schrödinger Equation with a nonlinear damping. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2377-2394. doi: 10.3934/cpaa.2014.13.2377
[11]

Patrick Martinez, Jean-Michel Roquejoffre. The rate of attraction of super-critical waves in a Fisher-KPP type model with shear flow. Communications on Pure & Applied Analysis, 2012, 11 (6) : 2445-2472. doi: 10.3934/cpaa.2012.11.2445
[12]

Wentao Huang, Jianlin Xiang. Soliton solutions for a quasilinear Schrödinger equation with critical exponent. Communications on Pure & Applied Analysis, 2016, 15 (4) : 1309-1333. doi: 10.3934/cpaa.2016.15.1309
[13]

Yinbin Deng, Wentao Huang. Positive ground state solutions for a quasilinear elliptic equation with critical exponent. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4213-4230. doi: 10.3934/dcds.2017179
[14]

Yinbin Deng, Shuangjie Peng, Li Wang. Existence of multiple solutions for a nonhomogeneous semilinear elliptic equation involving critical exponent. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 795-826. doi: 10.3934/dcds.2012.32.795
[15]

Ting Guo, Xianhua Tang, Qi Zhang, Zu Gao. Nontrivial solutions for the choquard equation with indefinite linear part and upper critical exponent. Communications on Pure & Applied Analysis, 2020, 19 (3) : 1563-1579. doi: 10.3934/cpaa.2020078
[16]

Björn Birnir, Kenneth Nelson. The existence of smooth attractors of damped and driven nonlinear wave equations with critical exponent , s = 5. Conference Publications, 1998, 1998 (Special) : 100-117. doi: 10.3934/proc.1998.1998.100
[17]

Zhaojuan Wang, Shengfan Zhou. Random attractor for stochastic non-autonomous damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 545-573. doi: 10.3934/dcds.2017022
[18]

Fengjuan Meng, Chengkui Zhong. Multiple equilibrium points in global attractor for the weakly damped wave equation with critical exponent. Discrete & Continuous Dynamical Systems - B, 2014, 19 (1) : 217-230. doi: 10.3934/dcdsb.2014.19.217
[19]

Wenmin Gong, Guangcun Lu. On Dirac equation with a potential and critical Sobolev exponent. Communications on Pure & Applied Analysis, 2015, 14 (6) : 2231-2263. doi: 10.3934/cpaa.2015.14.2231
[20]

Michinori Ishiwata. Existence of a stable set for some nonlinear parabolic equation involving critical Sobolev exponent. Conference Publications, 2005, 2005 (Special) : 443-452. doi: 10.3934/proc.2005.2005.443

2019 Impact Factor: 0.953

Tools

Metrics

  • PDF downloads (32)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences