The threshold of effective damping for semilinear wave equations
From MaRDI portal
Publication:5246788
DOI10.1002/mma.3126zbMath1316.35201arXiv1211.0731OpenAlexW2116411303MaRDI QIDQ5246788
Publication date: 22 April 2015
Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1211.0731
Critical exponents in context of PDEs (35B33) Initial value problems for second-order hyperbolic equations (35L15) Second-order semilinear hyperbolic equations (35L71)
Related Items (61)
Blow-up and lifespan estimates for a damped wave equation in the Einstein-de Sitter spacetime with nonlinearity of derivative type ⋮ Small data blow-up of semi-linear wave equation with scattering dissipation and time-dependent mass ⋮ A damping term for higher-order hyperbolic equations ⋮ A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass ⋮ Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data ⋮ A scale of critical exponents for semilinear waves with time-dependent damping and mass terms ⋮ Modified different nonlinearities for weakly coupled systems of semilinear effectively damped waves with different time-dependent coefficients in the dissipation terms ⋮ On the nonexistence of global solutions for critical semilinear wave equations with damping in the scattering case ⋮ The lifespan of solutions to semilinear damped wave equations in one space dimension ⋮ Scaling variables and asymptotic profiles for the semilinear damped wave equation with variable coefficients ⋮ On the Strauss index of semilinear Tricomi equation ⋮ Critical exponent for a class of semilinear damped wave equations with decaying in time propagation speed ⋮ A blow-up result for a semilinear wave equation with scale-invariant damping and mass and nonlinearity of derivative type ⋮ Global existence and blow-up for semilinear damped wave equations in three space dimensions ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques ⋮ The critical exponent(s) for the semilinear fractional diffusive equation ⋮ Weakly coupled system of semilinear wave equations with distinct scale-invariant terms in the linear part ⋮ Global existence for equivalent nonlinear special scale invariant damped wave equations ⋮ Sharp lifespan estimates of blowup solutions to semi-linear wave equations with time-dependent effective damping ⋮ Blowup for a damped wave equation with mass and general nonlinear memory ⋮ A competition on blow-up for semilinear wave equations with scale-invariant damping and nonlinear memory term ⋮ The lifespan estimates of classical solutions of one dimensional semilinear wave equations with characteristic weights ⋮ Critical exponent of Fujita type for semilinear wave equations in Friedmann–Lemaître–Robertson–Walker spacetime ⋮ The move from Fujita type exponent to a shift of it for a class of semilinear evolution equations with time-dependent damping ⋮ Blow-up of solutions to the semilinear wave equation with scale invariant damping on exterior domain ⋮ Blow-up solutions to the semilinear wave equation with overdamping term ⋮ Semilinear evolution models with scale-invariant friction and visco-elastic damping ⋮ Dissipative higher order hyperbolic equations ⋮ Small data blow-up for the wave equation with a time-dependent scale invariant damping and a cubic convolution for slowly decaying initial data ⋮ Scale-invariant semilinear damped wave models with mass term and integrable in time speed of propagation. ⋮ Global existence of solutions for semi-linear wave equation with scale-invariant damping and mass in exponentially weighted spaces ⋮ Critical exponent for the wave equation with a time-dependent scale invariant damping and a cubic convolution ⋮ Blow-up of solutions to the one-dimensional semilinear wave equation with damping depending on time and space variables ⋮ Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity ⋮ A note on \(L^p - L^q\) estimates for semilinear critical dissipative Klein-Gordon equations ⋮ Critical exponent for the semilinear wave equations with a damping increasing in the far field ⋮ Scattering and asymptotic order for the wave equations with the scale-invariant damping and mass ⋮ Small Data Solutions for Semilinear Waves with Time-Dependent Damping and Mass Terms ⋮ A shift in the strauss exponent for semilinear wave equations with a not effective damping ⋮ Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity ⋮ Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case ⋮ Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma ⋮ A classification of structural dissipations for evolution operators ⋮ Small data solutions for the Euler-Poisson-Darboux equation with a power nonlinearity ⋮ Improvement on the blow-up of the wave equation with the scale-invariant damping and combined nonlinearities ⋮ Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime ⋮ Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent ⋮ Global existence for semilinear wave equations with scaling invariant damping in 3-D ⋮ Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case ⋮ Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity ⋮ Fujita modified exponent for scale invariant damped semilinear wave equations ⋮ Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity ⋮ Remark on the blow-up of solutions for the semilinear wave equation with overdamping term ⋮ Remarks on asymptotic order for the linear wave equation with the scale-invariant damping and mass with 𝐿^{𝑟}-data ⋮ The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions ⋮ Advection versus diffusion in Richtmyer-Meshkov mixing ⋮ Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity ⋮ Asymptotic profiles and critical exponents for a semilinear damped plate equation with time-dependent coefficients ⋮ Sharp time decay rates on a hyperbolic plate model under effects of an intermediate damping with a time-dependent coefficient ⋮ NLWE with a special scale invariant damping in odd space dimension
Cites Work
- Unnamed Item
- Semi-linear wave equations with effective damping
- A scale-invariant Klein-Gordon model with time-dependent potential
- Asymptotic behavior of solutions to the semilinear wave equation with time-dependent damping
- Wave equations with time-dependent dissipation. II: Effective dissipation
- On the asymptotic behavior of solutions of semi-linear wave equations
- Critical exponent for the semilinear wave equation with time-dependent damping
- Global existence of solutions for semilinear damped wave equations in \(\mathbb R^N\) with noncompactly supported initial data
- Decay estimates of solutions for dissipative wave equations in \(\mathbb R^N\) with lower power nonlinearities
- \(L^p\)-\(L^q\) estimates for damped wave equations and their applications to semi-linear problem
- A class of dissipative wave equations with time-dependent speed and damping
- An application of \(L^p-L^q\) decay estimates to the semi-linear wave equation with parabolic-like structural damping
- The influence of a nonlinear memory on the damped wave equation
- A blow-up result for a nonlinear wave equation with damping: The critical case
- Biow-up of solutions of some nonlinear hyperbolic equations
- Solution representations for a wave equation with weak dissipation
- Critical exponent for a nonlinear wave equation with damping
This page was built for publication: The threshold of effective damping for semilinear wave equations
