Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass

被引:2
作者
Inui, Takahisa [1 ]
Mizutani, Haruya [1 ]
机构
[1] Osaka Univ, Dept Math, Grad Sch Sci, Toyonaka, Osaka 5600043, Japan
来源
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2021年 / 28卷 / 01期
关键词
Wave equation; Scale-invariant damping; Scattering; Energy critical nonlinearity; Strichartz estimates; TIME-DEPENDENT DISSIPATION; LIFE-SPAN; EXPONENT;
D O I
10.1007/s00030-020-00671-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the linear wave equation with the time-dependent scale-invariant damping and mass. We also treat the corresponding equation with the energy critical nonlinearity. Our aim is to show that the solution scatters to a modified linear wave solution and to obtain its asymptotic order.
引用
收藏
页数:33
相关论文
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[1]   Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass [J].
Takahisa Inui ;
Haruya Mizutani .
Nonlinear Differential Equations and Applications NoDEA, 2021, 28
[2]   REMARKS ON ASYMPTOTIC ORDER FOR THE LINEAR WAVE EQUATION WITH THE SCALE-INVARIANT DAMPING AND MASS WITH Lr-DATA [J].
Inui, Takahisa ;
Mizutani, Haruya .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (08) :3473-3484
[3]   The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions [J].
Imai, Takuto ;
Kato, Masakazu ;
Takamura, Hiroyuki ;
Wakasa, Kyouhei .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (10) :8387-8424
[4]   IMPROVEMENT ON THE BLOW-UP FOR A WEAKLY COUPLED WAVE EQUATIONS WITH SCALE-INVARIANT DAMPING AND MASS AND TIME DERIVATIVE NONLINEARITY [J].
Hamouda, Makram ;
Hamza, Mohamed Ali .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (06) :1468-1483
[5]   Blow-up for wave equation with the scale-invariant damping and combined nonlinearities [J].
Hamouda, Makram ;
Hamza, Mohamed Ali .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (01) :1127-1136
[6]   A COMPETITION ON BLOW-UP FOR SEMILINEAR WAVE EQUATIONS WITH SCALE-INVARIANT DAMPING AND NONLINEAR MEMORY TERM [J].
Chen, Wenhui ;
Fino, Ahmad Z. .
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (06) :1264-1285
[7]   THE LIFESPAN OF SOLUTIONS OF SEMILINEAR WAVE EQUATIONS WITH THE SCALE-INVARIANT DAMPING IN ONE SPACE DIMENSION [J].
Kato, Masakazu ;
Takamura, Hiroyuki ;
Wakasa, Kyouhei .
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2019, 32 (11-12) :659-678
[8]   A BLOW-UP RESULT FOR THE WAVE EQUATION: THE SCALE-INVARIANT DAMPING AND MASS TERM WITH COMBINED NONLINEARITIES [J].
Hamouda, Makram ;
Hamza, Mohamed Ali .
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2022, 12 (05) :1816-1841
[9]   Improvement on the Blow-Up for the Weakly Coupled Wave Equations with Scale-Invariant Damping and Time Derivative Nonlinearity [J].
Hamouda, Makram ;
Hamza, Mohamed Ali .
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (03)
[10]   Improvement on the Blow-Up for the Weakly Coupled Wave Equations with Scale-Invariant Damping and Time Derivative Nonlinearity [J].
Makram Hamouda ;
Mohamed Ali Hamza .
Mediterranean Journal of Mathematics, 2022, 19