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

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Takahisa Inui ◽  
Haruya Mizutani
Keyword(s):  
Wave Equations ◽  
Scale Invariant ◽  
Asymptotic Order

scholarly journals Global existence for equivalent nonlinear special scale invariant damped wave equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Vector Fields ◽  
Wave Equations ◽  
Small Data ◽  
Damped Wave Equation ◽  
Scale Invariant ◽  
Forcing Term ◽  
Time Existence

<p style='text-indent:20px;'>In this paper we give the notion of equivalent damped wave equations. As an application we study global in time existence for the solution of special scale invariant damped wave equation with small data. To gain such results, without radial assumption, we deal with Klainerman vector fields. In particular we can treat some potential behind the forcing term.</p>

Theory of damped wave models with integrable and decaying in time speed of propagation

2016 ◽  
Vol 13 (02) ◽  
pp. 417-439 ◽  
Author(s):  
Marcelo Rempel Ebert ◽  
Michael Reissig
Keyword(s):  
Cauchy Problem ◽  
Wave Equations ◽  
Propagation Speed ◽  
Time Dependent ◽  
Scale Invariant ◽  
The Cauchy Problem ◽  
Wave Models ◽  
Speed Of Propagation ◽  
Loss Of Regularity

We study the Cauchy problem for damped wave equations with a time-dependent propagation speed and dissipation. The model of interest is [Formula: see text] We assume [Formula: see text]. Then we propose a classification of dissipation terms in non-effective and effective. In each case we derive estimates for kinetic and elastic type energies by developing a suitable WKB analysis. Moreover, we show optimality of results by the aid of scale-invariant models. Finally, we explain by an example that in some estimates a loss of regularity appears.

scholarly journals Fujita modified exponent for scale invariant damped semilinear wave equations

2021 ◽  
Author(s):  
Felisia Angela Chiarello ◽  
Giovanni Girardi ◽  
Sandra Lucente
Keyword(s):  
Initial Data ◽  
Wave Equations ◽  
Nonlinear Term ◽  
Blow Up ◽  
Damping Coefficient ◽  
Damped Wave Equation ◽  
Scale Invariant ◽  
Decay Condition ◽  
Upper Bound Estimate ◽  
Pointwise Decay

AbstractThe aim of this paper is to prove a blow-up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term depends both on the damping coefficient and on the pointwise decay order of the initial data. In addition, we give an upper bound estimate for the lifespan of the solution. It depends not only on the exponent of the nonlinear term and not only on the damping coefficient but also on the size of the decay rate of the initial data.

scholarly journals The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions

2020 ◽  
Vol 269 (10) ◽  
pp. 8387-8424 ◽  
Author(s):  
Takuto Imai ◽  
Masakazu Kato ◽  
Hiroyuki Takamura ◽  
Kyouhei Wakasa
Keyword(s):  
Wave Equations ◽  
Scale Invariant ◽  
Semilinear Wave Equations ◽  
Two Space Dimensions
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