Finite-Time Blowup for Wave Equations with a Potential
From MaRDI portal
Publication:5317390
DOI10.1137/S0036141004440198zbMath1074.35075MaRDI QIDQ5317390
Qi S. Zhang, Borislav Yordanov
Publication date: 16 September 2005
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
semilinear wave equationcompactly supported initial datanonnegative potentialsubcritical nonlinear term
Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)
Related Items
On the asymptotic behavior of nonlinear waves in the presence of a short-range potential ⋮ Blow up for initial-boundary value problem of wave equation with a nonlinear memory in 1-D ⋮ Blow-up analysis for two kinds of nonlinear wave equations ⋮ Life span of small solutions to a system of wave equations ⋮ Finite time blow up for critical wave equations in high dimensions ⋮ Instability of steady states for nonlinear wave and heat equations ⋮ Approximation of quasilinear hyperbolic problems with discontinuous coefficients: an optimal error estimate ⋮ Blow-up of solutions to semilinear wave equations with variable coefficients and boundary ⋮ Concerning the Strauss conjecture for the subcritical and critical cases on the exterior domain in two space dimensions ⋮ Strauss exponent for semilinear wave equations with scattering space dependent damping ⋮ On a nonlinear scattering model ⋮ Global solvability for nonlinear wave equations with singular potential ⋮ Nonhomogeneous boundary-value problem for semilinear hyperbolic equation. Stability ⋮ Critical exponent for nonlinear damped wave equations with non-negative potential in 3D ⋮ Lifespan estimates for semilinear wave equations with space dependent damping and potential ⋮ The rescaling method for some quasilinear wave equations with the divergence forms of the nonlinearity ⋮ Integral Transform Approach to Time-Dependent Partial Differential Equations ⋮ On the Global Solutions of the Higgs Boson Equation ⋮ Variational approach to stability of semilinear wave equation with nonlinear boundary conditions ⋮ Finite lifespan of solutions of the semilinear wave equation in the Einstein–de Sitter spacetime ⋮ Variational methods in semilinear wave equation with nonlinear boundary conditions and stability questions ⋮ Life-Span of Solutions to Critical Semilinear Wave Equations ⋮ Solvability and stability of a semilinear wave equation with nonlinear boundary conditions ⋮ The rescaling method for some critical quasilinear wave equations with the divergence form of the nonlinearity ⋮ Blow-up of solutions of some nonlinear wave equations ⋮ Time optimal control problems for some non-smooth systems ⋮ On the critical behavior for inhomogeneous wave inequalities with Hardy potential in an exterior domain ⋮ Lifespan of solutions to semilinear damping wave equations in De Sitter spacetime ⋮ Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential ⋮ Optimal blowup time for controlled ordinary differential equations ⋮ Blow Up for Some Semilinear Wave Equations in Multi-space Dimensions ⋮ Variational analysis of semilinear plate equation with free boundary conditions