Space-time estimates on damped fractional wave equation
type: Item
instance of: scholarly article
title: Space-time estimates on damped fractional wave equation
zbMATH Open document ID: 1468.35227
DOI: 10.1155/2014/428909
author: Jiecheng Chen
author: Dashan Fan
author: Chunjie Zhang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We obtain space-time estimates on the solution \(u(t, x)\) to the Cauchy problem of damped fractional wave equation. We mainly focus on the linear equation. The almost everywhere convergence of the solution to linear equations as \(t \rightarrow 0^+\) is also studied, with the initial data satisfying certain regularity conditions.
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 7022376
Wikidata QID: Q59037972
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/428909
OpenAlex ID: W2052674569
cites work: Blow-Up Estimates for a Nonlinear Hyperbolic Heat Equation
cites work: On Strichartz estimates for Schrödinger operators in compact manifolds with boundary
cites work: Q4434430
cites work: Rapidly decaying solutions of the nonlinear Schrödinger equation
cites work: Hardy space estimates for the wave equation on compact Lie groups
cites work: Solutions for semilinear parabolic equations in \(L^ p\) and regularity of weak solutions of the Navier-Stokes system
cites work: Heat kernels and maximal lp—lqestimates for parabolic evolution equations
cites work: Endpoint Strichartz estimates
cites work: On existence and scattering with minimal regularity for semilinear wave equations
cites work: \(L^p-L^q\) estimates for the Klein-Gordon equation
cites work: Strong solutions to the nonlinear heat equation in homogeneous Besov spaces
cites work: Q3871351
cites work: Local Smoothing of Fourier Integral Operators and Carleson-Sjolin Estimates
cites work: \(L^p\)-estimates for the wave equation on the Heisenberg group
cites work: Existence of global solutions to the Cauchy problem for the semilinear dissipative wave equations
cites work: \(L^p\) estimates for the waves equation
cites work: Regularity properties of Fourier integral operators
cites work: STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS
cites work: Strichartz estimates for the Schrödinger equation with radial data
cites work: NON-UNIQUENESS FOR A CRITICAL NON-LINEAR HEAT EQUATION
cites work: Critical exponent for a nonlinear wave equation with damping
cites work: Inhomogeneous Strichartz estimates for the Schrödinger equation
cites work: Existence and non-existence of global solutions for a semilinear heat equation
cites work: Damped wave equation with a critical nonlinearity
cites work: Global existence of solutions for semilinear damped wave equations in \(\mathbb R^N\) with noncompactly supported initial data
cites work: Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
cites work: The \(L^{p}\)--\(L^{q}\) estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media
cites work: On the asymptotic behavior of solutions of semi-linear wave equations
cites work: Well-posedness of the Cauchy problem for the fractional power dissipative equations
cites work: Q4827105
cites work: \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
cites work: Q3025602
cites work: \(L^p\)-\(L^q\) estimates of solutions to the damped wave equation in 3-dimensional space and their application
cites work: Q3568256
cites work: A blow-up result for a nonlinear wave equation with damping: the critical case
cites work: Estimates on fractional power dissipative equations in function spaces
cites work: Strichartz type estimates for fractional heat equations
cites work: Q3878061
cites work: Q3923074
cites work: A local smoothing estimate for the Schrödinger equation
cites work: Q3860626
cites work: Pointwise convergence of solutions to Schr\"odinger equations
cites work: Regularity of solutions to the Schrödinger equation
cites work: Schrodinger Equations: Pointwise Convergence to the Initial Data
cites work: Q4112938
cites work: Theory of function spaces
cites work: Parabolic maximal functions associated with a distribution. II
cites work: Q3142876
cites work: Q5640160
cites work: On the Weighted Estimate of the Solution Associated with the Schrodinger Equation
description: scientific article; zbMATH DE number 7022376