Global existence and nonexistence in a system of Petrovsky
From MaRDI portal
Publication:5957731
DOI10.1006/JMAA.2001.7697zbMath1006.35070OpenAlexW2149412090MaRDI QIDQ5957731
Publication date: 2 March 2003
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jmaa.2001.7697
Critical exponents in context of PDEs (35B33) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Higher-order nonlinear hyperbolic equations (35L75)
Related Items (85)
Global existence and energy decay estimate of solutions for a class of nonlinear higher-order wave equation with general nonlinear dissipation and source term ⋮ The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term ⋮ Global existence and blow-up of solutions for a strongly damped Petrovsky system with nonlinear damping ⋮ Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ Existence, decay, and blow-up of solutions for a higher-order Kirchhoff-type equation with delay term ⋮ Exact thresholds for global existence to the nonlinear beam equations with and without a damping ⋮ On decay and blow-up of solutions for a nonlinear Petrovsky system with conical degeneration ⋮ A blow-up result in a nonlinear abstract evolution system with delay ⋮ Young measure solutions for a fourth-order wave equation with variable growth ⋮ Global existence and blow-up of solutions for logarithmic Klein-Gordon equation ⋮ Decay and blow up at infinite time of solutions for a logarithmic Petrovsky equation ⋮ Global existence of solutions for a coupled viscoelastic plate equation with degenerate damping terms ⋮ Optimal control problems for hyperbolic equations with damping terms involving p-Laplacian ⋮ A viscoelastic wave equation with delay and variable exponents: existence and nonexistence ⋮ On asymptotic behavior and blow-up of solutions for a nonlinear viscoelastic Petrovsky equation with positive initial energy ⋮ Global existence and blow-up of solutions for a Kirchhoff type plate equation with damping ⋮ Existence and blow up of solutions to a Petrovsky equation with memory and nonlinear source term ⋮ Blow up and global solutions for a quasilinear riser problem ⋮ GLOBAL SOLUTION AND BLOW-UP OF LOGARITHMIC KLEIN-GORDON EQUATION ⋮ A note on a class of 4th order hyperbolic problems with weak and strong damping and superlinear source term ⋮ Global existence and finite time blow-up for a class of thin-film equation ⋮ Blow-up of solutions to the fourth-order equation with variable-exponent nonlinear weak damping ⋮ Unnamed Item ⋮ Existence and blow up of solutions for a Petrovsky equation with variable-exponents ⋮ Breakdown for a Kirchhoff-type beam with a fractional boundary feedback ⋮ Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity ⋮ Well-posedness and dynamical properties for extensible beams with nonlocal frictional damping and polynomial nonlinearity ⋮ Lower bound for the lifespan of solutions for a class of fourth order wave equations ⋮ Global existence, uniform decay and blow-up of solutions for a system of Petrovsky equations ⋮ Blow-up phenomena for a class of extensible beam equations ⋮ Blow-up phenomena for a damped plate equation with logarithmic nonlinearity ⋮ Behavior of solutions to a Petrovsky equation with damping and variable-exponent sources ⋮ Global existence, asymptotic behavior and blow-up of solutions for a suspension bridge equation with nonlinear damping and source terms ⋮ Energy Decay for a Type of Plate Equation with Degenerate Energy Damping and Source Term ⋮ Stability results for a system of nonlinear viscoelastic plate equations with nonlinear frictional damping and logarithmic source terms ⋮ Global solutions and blow-up for a class of strongly damped wave equations systems ⋮ Blow up result for a viscoelatic plate equation with nonlinear source ⋮ The existence, general decay and blow-up for a plate equation with nonlinear damping and a logarithmic source term ⋮ Global existence and blowup of solutions for a class of nonlinear higher-order wave equations ⋮ Existence and stability results of a plate equation with nonlinear damping and source term ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Finite time blow-up for a nonlinear viscoelastic Petrovsky equation with high initial energy ⋮ On the general decay of a nonlinear viscoelastic plate equation with a strong damping and \(\vec{p}(x,t)\)-Laplacian ⋮ Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipation ⋮ Unnamed Item ⋮ Global existence of a coupled Euler-Bernoulli plate system with variable coefficients ⋮ Blow-up of solution for a nonlinear Petrovsky type equation with memory ⋮ Decay and blow-up for a viscoelastic wave equation of variable coefficients with logarithmic nonlinearity ⋮ Global existence and asymptotic behaviour for systems of nonlinear hyperbolic equations ⋮ Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term ⋮ Existence, nonexistence, and stability of solutions for a delayed plate equation with the logarithmic source ⋮ Existence and asymptotic stability of solutions for hyperbolic differential inclusions with a source term ⋮ Blow up solutions to a system of higher-order Kirchhoff-type equations with positive initial energy ⋮ Blow-up of solutions for a system of higher-order nonlinear Kirchhoff-type equations ⋮ Global existence and energy decay estimate of solutions for a higher-order Kirchhoff type equation with damping and source term ⋮ Existence and asymptotic behavior of global solutions for a class of nonlinear higher-order wave equation ⋮ Existence and asymptotic behavior for systems of nonlinear hyperbolic equations ⋮ Asymptotic stability and blow up of solutions for a Petrovsky inverse source problem with dissipative boundary condition ⋮ Global existence and blow-up for the Euler-Bernoulli plate equation with variable coefficients ⋮ Asymptotic energy estimates for nonlinear Petrovsky plate model subject to viscoelastic damping ⋮ Blow up of solutions for a nonlinear Petrovsky type equation with time-dependent coefficients ⋮ A nonlinear viscoelastic plate equation with \(\vec{p} ( x , t )\)-Laplace operator: blow up of solutions with negative initial energy ⋮ Unnamed Item ⋮ Existence and blow-up of solutions for von Karman equations with time delay and variable exponents ⋮ Existence and stability results of a nonlinear Timoshenko equation with damping and source terms ⋮ Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ Global nonexistence for a semilinear Petrovsky equation ⋮ Asymptotic stability and blowup of solutions for a class of viscoelastic inverse problem with boundary feedback ⋮ Network-based control of a semilinear damped beam equation under point and pointlike measurements ⋮ A class of fourth-order hyperbolic equations with strongly damped and nonlinear logarithmic terms ⋮ Unnamed Item ⋮ General decay rate of a weakly dissipative viscoelastic equation with a general damping ⋮ Global attractor for a class of Kirchhoff models ⋮ General decay and blow-up results for nonlinear fourth-order integro-differential equation ⋮ Polynomial-exponential stability and blow-up solutions to a nonlinear damped viscoelastic Petrovsky equation ⋮ Lifespan for solutions to 4-th order hyperbolic systems with time dependent coefficients ⋮ Global existence and exponential decay for a viscoelastic Petrovsky system ⋮ Finite-dimensional attractors for the Kirchhoff models ⋮ Global attractors and their Hausdorff dimensions for a class of Kirchhoff models ⋮ Finite-dimensional attractors for the Kirchhoff models with critical exponents ⋮ Lower bounds for blow-up time of two nonlinear wave equations ⋮ Blow-up of solutions for a nonlinear Petrovsky type equation with initial data at arbitrary high energy level ⋮ New general decay results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ Existence and energy decay of solutions for the Euler-Bernoulli viscoelastic equation with a delay
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Global existence and internal nonlinear damping for a Petrovsky system
- Existence of a solution of the wave equation with nonlinear damping and source terms
- Analysis and control of nonlinear infinite dimensional systems
- Energy decay for a damped nonlinear hyperbolic equation
- Energy decay for a damped nonlinear coupled system
This page was built for publication: Global existence and nonexistence in a system of Petrovsky
