scholarly journals Critical exponent of Fujita-type for semilinear wave equations in Friedmann-Lemaître-Robertson-Walker spacetime

2021 ◽  
Author(s):  
Marcelo Ebert ◽  
Jorge Marques
Keyword(s):  
Wave Equation ◽  
Critical Exponent ◽  
Wave Equations ◽  
Small Data ◽  
Semilinear Wave Equations

We consider the nonlinear massless wave equation belonging to some family of the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We prove the global in time small data solutions for supercritical powers in the case of decelerating expansion universe.

A Modified Test Function Method for Damped Wave Equations

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Marcello D’Abbicco ◽  
Sandra Lucente
Keyword(s):  
Wave Equation ◽  
Global Existence ◽  
Critical Exponent ◽  
Function Method ◽  
Wave Equations ◽  
Time Dependent ◽  
Small Data ◽  
Test Function ◽  
Test Function Method ◽  
Modified Test

AbstractIn this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global existence of small data solutions.

Global well-posedness and self-similarity for semilinear wave equations in a time-weighted framework of Besov type

2020 ◽  
Vol 17 (01) ◽  
pp. 123-139
Author(s):  
Lucas C. F. Ferreira ◽  
Jhean E. Pérez-López
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Besov Spaces ◽  
Wave Equations ◽  
Well Posedness ◽  
Self Similarity ◽  
Semilinear Wave Equations ◽  
Semilinear Wave Equation

We show global-in-time well-posedness and self-similarity for the semilinear wave equation with nonlinearity [Formula: see text] in a time-weighted framework based on the larger family of homogeneous Besov spaces [Formula: see text] for [Formula: see text]. As a consequence, in some cases of the power [Formula: see text], we cover a initial-data class larger than in some previous results. Our approach relies on dispersive-type estimates and a suitable [Formula: see text]-product estimate in Besov spaces.

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>

scholarly journals Critical Exponent for Semilinear Wave Equations with Space-Dependent Potential

2009 ◽  
Vol 52 (3) ◽  
pp. 411-435 ◽  
Author(s):  
Ryo Ikehata ◽  
Grozdena Todorova ◽  
Borislav Yordanov
Keyword(s):  
Critical Exponent ◽  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Dependent Potential
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