scholarly journals A Sharp Lorentz-Invariant Strichartz Norm Expansion for the Cubic Wave Equation in ℝ1+3

2020 ◽  
Vol 71 (2) ◽  
pp. 451-483
Author(s):  
Giuseppe Negro
Keyword(s):  
Wave Equation ◽  
Asymptotic Formula ◽  
Minkowski Space ◽  
Strichartz Estimate ◽  
Sharp Constant

Abstract We provide an asymptotic formula for the maximal Strichartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz estimate. We calculate the constant in the second term, which differs depending on whether the equation is focussing or defocussing. The sign of this coefficient also changes accordingly.

Numerical solution of the wave equation on 1+1 Minkowski space-time with scri-fixing conformal compatification

2010 ◽  
Author(s):  
A. Cruz-Osorio ◽  
F. D. Lora-Clavijo ◽  
F. S. Guzmán ◽  
H. A. Morales-Tecotl ◽  
L. A. Urena-Lopez ◽  
...  
Keyword(s):  
Wave Equation ◽  
Numerical Solution ◽  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals Fractal Strichartz estimate for the wave equation

2017 ◽  
Vol 150 ◽  
pp. 61-75
Author(s):  
Chu-Hee Cho ◽  
Seheon Ham ◽  
Sanghyuk Lee
Keyword(s):  
Wave Equation ◽  
Strichartz Estimate

scholarly journals On the supercritical defocusing NLW outside a ball

2021 ◽  
Vol 11 (4) ◽  
Author(s):  
Piero D’Ancona
Keyword(s):  
Wave Equation ◽  
Large Time ◽  
Dirichlet Boundary ◽  
Strichartz Estimate ◽  
Energy Inequality ◽  
Dirichlet Boundary Conditions ◽  
Linear Wave ◽  
Linear Wave Equation ◽  
Penrose Transform ◽  
Dependent Potential

AbstractWe study a defocusing semilinear wave equation, with a power nonlinearity $$|u|^{p-1}u$$ | u | p - 1 u , defined outside the unit ball of $$\mathbb {R}^{n}$$ R n , $$n\ge 3$$ n ≥ 3 , with Dirichlet boundary conditions. We prove that if $$p>n+3$$ p > n + 3 and the initial data are nonradial perturbations of large radial data, there exists a global smooth solution. The solution is unique among energy class solutions satisfying an energy inequality. The main tools used are the Penrose transform and a Strichartz estimate for the exterior linear wave equation perturbed with a large, time dependent potential.

scholarly journals A sharp Sobolev-Strichartz estimate for the wave equation

2015 ◽  
Vol 22 (0) ◽  
pp. 46-54
Author(s):  
Chris Jeavons ◽  
Neal Bez
Keyword(s):  
Wave Equation ◽  
Strichartz Estimate

scholarly journals Strong Exponential Attractors for Weakly Damped Semilinear Wave Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Cuncai Liu ◽  
Fengjuan Meng ◽  
Chang Zhang
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Strichartz Estimate ◽  
Exponential Attractor ◽  
Damped Wave Equation ◽  
Exponential Attractors ◽  
Bounded Smooth Domain ◽  
Strong Energy ◽  
Bounded Smooth ◽  
Recent Extension

In this paper, we investigate the longtime dynamics for the damped wave equation in a bounded smooth domain of ℝ3. The exponential attractor is investigated in a strong energy space for the case of subquintic nonlinearity, which is based on the recent extension of the Strichartz estimate for the case of a bounded domain. The results obtained complete some previous works.

Weighted Strichartz estimate for the wave equation

2000 ◽  
Vol 330 (5) ◽  
pp. 349-354
Author(s):  
Piero D'Ancona ◽  
Vladimir Georgiev ◽  
Hideo Kubo
Keyword(s):  
Wave Equation ◽  
Strichartz Estimate

A review: The Laplacian and the d’Alembertian

2017 ◽  
Author(s):  
Christopher D. Sogge
Keyword(s):  
Wave Equation ◽  
Euclidean Space ◽  
Fundamental Solution ◽  
Minkowski Space ◽  
Riemannian Manifolds ◽  
Wave Operator ◽  
Wave Equations ◽  
Fundamental Solutions ◽  
Specific Function ◽  
Solutions Of Wave Equations

This chapter reviews the Laplacian and the d'Alembertian. It begins with a brief discussion on the solution of wave equation both in Euclidean space and on manifolds and how this knowledge can be used to derive properties of eigenfunctions on Riemannian manifolds. A key step in understanding properties of solutions of wave equations on manifolds is to compute the types of distributions that include the fundamental solution of the wave operator in Minkowski space (d'Alembertian), with a specific function for the Euclidean Laplacian on Rn. The chapter also reviews another equation involving the Laplacian, before discussing the fundamental solutions of the d'Alembertian in R1+n.

Heavy Tails of Discounted Aggregate Claims in the Continuous-Time Renewal Model

2007 ◽  
Vol 44 (02) ◽  
pp. 285-294 ◽  
Author(s):  
Qihe Tang
Keyword(s):  
Asymptotic Formula ◽  
Continuous Time ◽  
Heavy Tails ◽  
Tail Behavior ◽  
Renewal Model ◽  
Discounted Aggregate Claims ◽  
Aggregate Claims ◽  
Tail Asymptotic

We study the tail behavior of discounted aggregate claims in a continuous-time renewal model. For the case of Pareto-type claims, we establish a tail asymptotic formula, which holds uniformly in time.

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