scholarly journals Long-time existence for semilinear wave equations with the inverse-square potential

2022 ◽  
Vol 309 ◽  
pp. 98-141
Author(s):  
Wei Dai ◽  
Daoyuan Fang ◽  
Chengbo Wang
Keyword(s):  
Wave Equations ◽  
Semilinear Wave Equations ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

scholarly journals The lifespan for 3-dimensional quasilinear wave equations in exterior domains

2014 ◽  
Vol 26 (6) ◽  
Author(s):  
John Helms ◽  
Jason Metcalfe
Keyword(s):  
Wave Equations ◽  
Energy Estimates ◽  
Exterior Domains ◽  
Small Initial Data ◽  
3 Dimensional ◽  
Long Time Existence ◽  
Homogeneous Wave ◽  
Long Time ◽  
Quasilinear Wave Equations ◽  
Time Existence

AbstractThis article focuses on long-time existence for quasilinear wave equations with small initial data in exterior domains. The nonlinearity is permitted to fully depend on the solution at the quadratic level, rather than just the first and second derivatives of the solution. The corresponding lifespan bound in the boundaryless case is due to Lindblad, and Du and Zhou first proved such long-time existence exterior to star-shaped obstacles. Here we relax the hypothesis on the geometry and only require that there is a sufficiently rapid decay of local energy for the linear homogeneous wave equation, which permits some domains that contain trapped rays. The key step is to prove useful energy estimates involving the scaling vector field for which the approach of the second author and Sogge provides guidance.

scholarly journals Long-Time Existence for Semi-linear Beam Equations on Irrational Tori

2021 ◽  
Author(s):  
Joackim Bernier ◽  
Roberto Feola ◽  
Benoît Grébert ◽  
Felice Iandoli
Keyword(s):  
Long Time Existence ◽  
Beam Equations ◽  
Long Time ◽  
Time Existence

Evolving inextensible and elastic curves with clamped ends under the second-order evolution equation in ℝ2

2018 ◽  
Vol 3 (1) ◽  
pp. 14-18 ◽  
Author(s):  
Chun-Chi Lin ◽  
Yang-Kai Lue
Keyword(s):  
Evolution Equation ◽  
Convergent Subsequence ◽  
Second Order ◽  
Plane Curves ◽  
Smooth Solutions ◽  
Fixed Position ◽  
Elastic Curves ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence

Abstract For any given C2-smooth initial open curves with fixed position and fixed tangent at the boundary points, we obtain the long-time existence of smooth solutions under the second-order evolution of plane curves. Moreover, the asymptotic limit of a convergent subsequence is an inextensible elastica.

scholarly journals Long-time existence of the edge Yamabe flow

2019 ◽  
Vol 71 (2) ◽  
pp. 651-688 ◽  
Author(s):  
Eric BAHUAUD ◽  
Boris VERTMAN
Keyword(s):  
Yamabe Flow ◽  
Long Time Existence ◽  
Long Time ◽  
Time Existence
Sign in / Sign up

Export Citation Format

Share Document