scholarly journals Well posedness and control of semilinear wave equations with iterated logarithms

1999 ◽  
Vol 4 ◽  
pp. 37-56 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Vilmos Komornik ◽  
Paola Loreti
Keyword(s):  
Wave Equations ◽  
Well Posedness ◽  
Semilinear Wave Equations ◽  
Iterated Logarithms ◽  
And Control

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 One-sided and internal controllability of semilinear wave equations with infinitely iterated logarithms

2002 ◽  
Vol 8 (3) ◽  
pp. 745-756 ◽  
Author(s):  
Piermarco Cannarsa ◽  
◽  
Vilmos Komornik ◽  
Paola Loreti ◽  
◽  
...  
Keyword(s):  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Iterated Logarithms

scholarly journals On averaged exponential integrators for semilinear wave equations with solutions of low-regularity

2021 ◽  
Vol 2 (2) ◽  
Author(s):  
Simone Buchholz ◽  
Benjamin Dörich ◽  
Marlis Hochbruck
Keyword(s):  
Error Analysis ◽  
Classical Solution ◽  
Error Bounds ◽  
Standard Error ◽  
Wave Equations ◽  
Time Integration ◽  
Well Posedness ◽  
Numerical Examples ◽  
Low Regularity ◽  
Semilinear Wave Equations

AbstractIn this paper we introduce a class of second-order exponential schemes for the time integration of semilinear wave equations. They are constructed such that the established error bounds only depend on quantities obtained from a well-posedness result of a classical solution. To compensate missing regularity of the solution the proofs become considerably more involved compared to a standard error analysis. Key tools are appropriate filter functions as well as the integration-by-parts and summation-by-parts formulas. We include numerical examples to illustrate the advantage of the proposed methods.

Sign in / Sign up

Export Citation Format

Share Document