Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension

Frank Merle; Hatem Zaag

doi:10.1353/ajm.2012.0021

Existence and classification of characteristic points at blow-up for a semilinear wave equation in one space dimension

American Journal of Mathematics ◽

10.1353/ajm.2012.0021 ◽

2012 ◽

Vol 134 (3) ◽

pp. 581-648 ◽

Cited By ~ 26

Author(s):

Frank Merle ◽

Hatem Zaag

Keyword(s):

Wave Equation ◽

Space Dimension ◽

Blow Up ◽

Semilinear Wave Equation ◽

Characteristic Points ◽

One Space Dimension

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Blow-up Rate for a Semilinear Wave Equation with Exponential Nonlinearity in One Space Dimension

Partial Differential Equations Arising from Physics and Geometry ◽

10.1017/9781108367639.001 ◽

2019 ◽

pp. 1-32

Author(s):

Asma Azaiez ◽

Nader Masmoudi ◽

Hatem Zaag

Keyword(s):

Wave Equation ◽

Space Dimension ◽

Blow Up ◽

Exponential Nonlinearity ◽

Semilinear Wave Equation ◽

Blow Up Rate ◽

One Space Dimension

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Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension

Journal of Functional Analysis ◽

10.1016/j.jfa.2007.03.007 ◽

2007 ◽

Vol 253 (1) ◽

pp. 43-121 ◽

Cited By ~ 35

Author(s):

Frank Merle ◽

Hatem Zaag

Keyword(s):

Wave Equation ◽

Space Dimension ◽

Blow Up ◽

Semilinear Wave Equation ◽

One Space Dimension

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𝒞1,αRegularity of the Blow-Up Curve at Non Characteristic Points for the One Dimensional Semilinear Wave Equation

Communications in Partial Differential Equations ◽

10.1080/03605300802234937 ◽

2008 ◽

Vol 33 (8) ◽

pp. 1540-1548 ◽

Cited By ~ 2

Author(s):

Nejla Nouaili

Keyword(s):

Wave Equation ◽

Blow Up ◽

One Dimensional ◽

Semilinear Wave Equation ◽

Characteristic Points ◽

The One

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Openness of the Set of Non-characteristic Points and Regularity of the Blow-up Curve for the 1 D Semilinear Wave Equation

Communications in Mathematical Physics ◽

10.1007/s00220-008-0532-3 ◽

2008 ◽

Vol 282 (1) ◽

pp. 55-86 ◽

Cited By ~ 27

Author(s):

Frank Merle ◽

Hatem Zaag

Keyword(s):

Wave Equation ◽

Blow Up ◽

Semilinear Wave Equation ◽

Characteristic Points

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Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2019108 ◽

2019 ◽

Vol 18 (5) ◽

pp. 2397-2408

Author(s):

Asma Azaiez ◽

Keyword(s):

Wave Equation ◽

Blow Up ◽

Semilinear Wave Equation ◽

Characteristic Points ◽

Vector Valued

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Construction of a Multisoliton Blowup Solution to the Semilinear Wave Equation in One Space Dimension

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.21452 ◽

2013 ◽

Vol 66 (10) ◽

pp. 1541-1581 ◽

Cited By ~ 22

Author(s):

Raphaël Côte ◽

Hatem Zaag

Keyword(s):

Wave Equation ◽

Space Dimension ◽

Blowup Solution ◽

Semilinear Wave Equation ◽

One Space Dimension

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On the existence of periodic solutions for semilinear wave equation on a ball in n with the space dimension n odd

Nonlinear Analysis ◽

10.1016/0362-546x(94)e0069-s ◽

1995 ◽

Vol 24 (2) ◽

pp. 241-250 ◽

Cited By ~ 6

Author(s):

A.K. Ben-Naoum ◽

J. Berkovits

Keyword(s):

Wave Equation ◽

Periodic Solutions ◽

Space Dimension ◽

Semilinear Wave Equation ◽

Existence Of Periodic Solutions

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Convergence of a blow-up curve for a semilinear wave equation

Discrete & Continuous Dynamical Systems - S ◽

10.3934/dcdss.2020388 ◽

2018 ◽

Vol 0 (0) ◽

pp. 0-0

Author(s):

Takiko Sasaki ◽

Keyword(s):

Wave Equation ◽

Blow Up ◽

Semilinear Wave Equation

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On similarity solutions and blow-up spectra for a semilinear wave equation

Quarterly of Applied Mathematics ◽

10.1090/qam/1999839 ◽

2003 ◽

Vol 61 (3) ◽

pp. 583-600 ◽

Cited By ~ 13

Author(s):

V. A. Galaktionov ◽

S. I. Pohozaev

Keyword(s):

Wave Equation ◽

Blow Up ◽

Similarity Solutions ◽

Semilinear Wave Equation

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Energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear source

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.4766 ◽

2018 ◽

Vol 41 (7) ◽

pp. 2639-2653 ◽

Cited By ~ 1

Author(s):

Lingwei Ma ◽

Zhong Bo Fang

Keyword(s):

Wave Equation ◽

Blow Up ◽

Energy Decay ◽

Decay Estimates ◽

Nonlinear Source ◽

Semilinear Wave Equation ◽

Strongly Damped

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