On potential wells and vacuum isolating of solutions for semilinear wave equations
From MaRDI portal
Publication:1399887
DOI10.1016/S0022-0396(02)00020-7zbMath1024.35078OpenAlexW1976383535MaRDI QIDQ1399887
Publication date: 30 July 2003
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00020-7
Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) A priori estimates in context of PDEs (35B45)
Related Items (94)
The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term ⋮ Global results for semilinear hyperbolic equations with damping term on manifolds with conical singularity ⋮ Global existence and blow-up for the pseudo-parabolic \(p(x)\)-Laplacian equation with logarithmic nonlinearity ⋮ Existence and nonexistence of global solutions for logarithmic hyperbolic equation ⋮ Global existence and blow-up of solutions for logarithmic Klein-Gordon equation ⋮ Dynamics of nonlinear hyperbolic equations of Kirchhoff type ⋮ Global existence and nonexistence of solution for Cauchy problem of multidimensional double dispersion equations ⋮ Global existence of solution for Cauchy problem of multidimensional generalized double dispersion equations ⋮ On potential wells to a semilinear hyperbolic equation with damping and conical singularity ⋮ Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations ⋮ Well-posedness of solutions for the dissipative Boussinesq equation with logarithmic nonlinearity ⋮ A class of fourth-order parabolic equation with arbitrary initial energy ⋮ Global existence, blow up and extinction for a class of thin-film equation ⋮ Degenerate Kirchhoff-type hyperbolic problems involving the fractional Laplacian ⋮ Global existence, finite time blow-up, and vacuum isolating phenomenon for a class of thin-film equation ⋮ Degenerate Kirchhoff-type diffusion problems involving the fractional \(p\)-Laplacian ⋮ A class of fourth-order parabolic equations with logarithmic nonlinearity ⋮ Blow-up for a damped \(p\)-Laplacian type wave equation with logarithmic nonlinearity ⋮ Fourth order wave equations with nonlinear strain and source terms ⋮ Blow up and blow up time for degenerate Kirchhoff-type wave problems involving the fractional Laplacian with arbitrary positive initial energy ⋮ General decay and blow-up results for a class of nonlinear pseudo-parabolic equations with viscoelastic term ⋮ Vacuum isolating and blow-up analysis for edge hyperbolic system on edge Sobolev spaces ⋮ Global existence and nonexistence of solutions for semilinear wave equation with a new condition ⋮ Global existence and finite time blowup for a fractional pseudo-parabolic \(p\)-Laplacian equation ⋮ On family of potential wells and applications to semilinear hyperbolic equations and parabolic equations ⋮ Vacuum isolating, blow up threshold, and asymptotic behavior of solutions for a nonlocal parabolic equation ⋮ Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity ⋮ Initial boundary value problem for a damped wave equation with logarithmic nonlinearity ⋮ Higher regularity and finite time blow-up to nonlocal pseudo-parabolic equation with conical degeneration ⋮ Blow‐up and energy decay for a class of wave equations with nonlocal Kirchhoff‐type diffusion and weak damping ⋮ Global existence, general decay and blow-up for a nonlinear wave equation with logarithmic source term and fractional boundary dissipation ⋮ The Cauchy problem for Choquard equation with an inverse‐square potential ⋮ Global existence and finite time blow‐up for the heat flow of H‐system with constant mean curvature ⋮ Global existence and finite-time blowup for a mixed pseudo-parabolic \(r(x)\)-Laplacian equation ⋮ Global existence and finite time blowup for a mixed pseudo-parabolic \(p\)-Laplacian type equation ⋮ Initial boundary value problem of pseudo‐parabolic Kirchhoff equations with logarithmic nonlinearity ⋮ The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term ⋮ Global existence and blow-up of solutions to a class of nonlocal parabolic equations ⋮ Ill-posedness of nonlinear parabolic equation with critical initial condition ⋮ Multidimensional viscoelasticity equations with nonlinear damping and source terms. ⋮ Global existence and finite time blow-up of solutions for the semilinear pseudo-parabolic equation with a memory term ⋮ Instability of the stationary solutions of generalized dissipative Boussinesq equation. ⋮ Global existence, finite time blow-up and vacuum isolating phenomena for semilinear parabolic equation with conical degeneration ⋮ Global existence and blow-up of solutions for nonlinear Klein-Gordon equation with damping term and nonnegative potentials ⋮ Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation ⋮ Global existence and nonexistence of solutions for quasilinear parabolic equation ⋮ Global existence, nonexistence, and decay of solutions for a viscoelastic wave equation with nonlinear boundary damping and source terms ⋮ Threshold results for the existence of global and blow-up solutions to Kirchhoff equations with arbitrary initial energy ⋮ Blow-up and global existence of solutions to a parabolic equation associated with the fraction \(p\)-Laplacian ⋮ Global existence and blow-up for a Kirchhoff-type hyperbolic problem with logarithmic nonlinearity ⋮ Asymptotic behavior of global solutions to a class of mixed pseudo-parabolic Kirchhoff equations ⋮ Well-posedness of nonlinear wave equation with combined power-type nonlinearities ⋮ The Dirichlet-Cauchy problem for nonlinear hyperbolic equations in a domain with edges ⋮ Some sharp results about the global existence and blowup of solutions to a class of coupled pseudo-parabolic equations ⋮ Blow-up phenomena for a class of fourth order parabolic equation ⋮ ON POTENTIAL WELLS AND VACUUM ISOLATING OF SOLUTIONS FOR SPACE-FRACTIONAL WAVE EQUATIONS ⋮ Invariance solutions and blow-up property for edge degenerate pseudo-hyperbolic equations in edge Sobolev spaces ⋮ A class of fourth order wave equations with dissipative and nonlinear strain terms ⋮ Qualitative analysis for a degenerate Kirchhoff-type diffusion equation involving the fractional \(p\)-Laplacian ⋮ Infinite sharp conditions by Nehari manifolds for nonlinear Schrödinger equations ⋮ Global existence and blow-up of weak solutions for a class of fractional \(p\)-Laplacian evolution equations ⋮ Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein-Gordon equation with dissipative term ⋮ Potential well method for Cauchy problem of generalized double dispersion equations ⋮ Asymptotic behavior for a fourth-order parabolic equation involving the Hessian ⋮ Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential ⋮ Initial boundary value problem for semilinear hyperbolic equations and parabolic equations with critical initial data ⋮ Global existence and asymptotic behavior of solutions for the double dispersive-dissipative wave equation with nonlinear damping and source terms ⋮ On potential wells and applications to semilinear hyperbolic equations and parabolic equations ⋮ Global existence, asymptotic behavior and blow-up of solutions for coupled Klein-Gordon equations with damping terms ⋮ Invariance and existence analysis for semilinear hyperbolic equations with damping and conical singularity ⋮ Global well-posedness for semilinear hyperbolic equations with dissipative term ⋮ Unnamed Item ⋮ Global existence and nonexistence of the initial-boundary value problem for the dissipative Boussinesq equation ⋮ GLOBAL EXISTENCE AND FINITE TIME BLOW-UP OF SOLUTIONS TO A NONLOCAL P-LAPLACE EQUATION ⋮ Behavior of solutions to a fourth-order nonlinear parabolic equation with logarithmic nonlinearity ⋮ Well-posedness of solutions for the sixth-order Boussinesq equation with linear strong damping and nonlinear source ⋮ Analysis of a pseudo-parabolic equation by potential wells ⋮ Initial boundary value problem of a class of mixed pseudo-parabolic Kirchhoff equations ⋮ Global existence and non-existence analyses to a nonlinear Klein-Gordon system with damping terms under positive initial energy ⋮ Hyperbolic and parabolic equations with several opposite-sign source at critical initial energy level in heat and vibrating systems ⋮ Global existence and non-existence analyses for a semilinear edge degenerate parabolic equation with singular potential term ⋮ Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity ⋮ Existence of the global solution for fractional logarithmic Schrödinger equation ⋮ Global solutions and blow up solutions to a class of pseudo-parabolic equations with nonlocal term ⋮ Initial-boundary value problem for a fourth-order plate equation with Hardy-Hénon potential and polynomial nonlinearity ⋮ A family of potential wells for a wave equation ⋮ Global well-posedness for the nonlinear damped wave equation with logarithmic type nonlinearity ⋮ Degenerate Kirchhoff-type wave problems involving the fractional Laplacian with nonlinear damping and source terms ⋮ Cauchy problem of nonlinear Klein-Gordon equations with general nonlinearities ⋮ A \(p\)-Laplace equation with logarithmic nonlinearity at high initial energy level ⋮ Global existence and blow-up of solutions for a \(\mathtt{p}\)-Kirchhoff type parabolic equation with logarithmic nonlinearity ⋮ Global existence, blow-up in finite time and vacuum isolating phenomena for a system of semilinear wave equations associated with the helical flows of Maxwell fluid ⋮ Unnamed Item ⋮ Well-posedness of solutions for a class of quasilinear wave equations with structural damping or strong damping
Cites Work
- Unnamed Item
- Unnamed Item
- Saddle points and instability of nonlinear hyperbolic equations
- On global solution of nonlinear hyperbolic equations
- Blow-up theorems for nonlinear wave equations
- Existence and nonexistence of global solutions for nonlinear parabolic equations
- REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
- Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
- Some remarks on the wave equations with nonlinear damping and source terms
- Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
This page was built for publication: On potential wells and vacuum isolating of solutions for semilinear wave equations