Blow-up result for a semilinear wave equation with a nonlinear memory term

DOI10.1007/978-3-030-61346-4_4zbMath1461.35068OpenAlexW3126302403MaRDI QIDQ2662134

Wenhui Chen, Alessandro Palmieri

Publication date: 9 April 2021

Full work available at URL: https://doi.org/10.1007/978-3-030-61346-4_4

zbMATH Keywords

Riemann-Liouville fractional integralnonlinear memory termiteration argumentgeneralized Strauss exponent

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Integro-partial differential equations (35R09) Second-order semilinear hyperbolic equations (35L71)

Related Items

Blow-up of energy solutions for the semilinear generalized Tricomi equation with nonlinear memory term ⋮ Lifespan estimates for local solutions to the semilinear wave equation in Einstein–de Sitter spacetime ⋮ 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 ⋮ Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The beam equation with nonlinear memory
• Improved Kato's lemma on ordinary differential inequality and its application to semilinear wave equations
• The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions
• On a recent result of Cazenave, Dickstein and Weissler
• Critical exponent for damped wave equations with nonlinear memory
• A nonlocal in time parabolic system whose Fujita critical exponent is not given by scaling
• Nonexistence of global solutions to semilinear wave equations in high dimensions
• Blow-up solutions of second-order differential inequalities with a nonlinear memory term
• Finite-time blow-up for solutions of nonlinear wave equations
• Existence in the large for \(cmu=F(u)\) in two space dimensions
• Nonlinear scattering theory at low energy
• Life span of classical solutions to \(u_{tt} - u_{xx} =| u|^{1+\alpha}\)
• Blow-up of solutions of nonlinear wave equations in three space dimensions
• Life span of classical solutions to \(\square u = | u | ^ p\) in two space dimensions
• Critical curve for \(p\)-\(q\) systems of nonlinear wave equations in three space dimensions
• Blow-up of solutions to critical semilinear wave equations with variable coefficients
• An elementary proof of the blow-up for semilinear wave equation in high space dimensions
• Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case
• Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms
• An elementary proof of Strauss conjecture
• A wave equation with structural damping and nonlinear memory
• Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities
• The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions
• Blow up for initial-boundary value problem of wave equation with a nonlinear memory in 1-D
• Finite time blow up for critical wave equations in high dimensions
• Blow-up of solutions for a time-space fractional evolution system
• An equation whose Fujita critical exponent is not given by scaling
• The influence of a nonlinear memory on the damped wave equation
• Blow up of solutions to semilinear wave equations with critical exponent in high dimensions
• Asymptotically self-similar global solutions of a damped wave equation with nonlinear memory
• Qualitative properties of solutions to a nonlocal evolution system
• Qualitative properties of solutions to a time-space fractional evolution equation
• Existence and blow-up of solutions for damped ave system with nonlinear memory
• Blow-up for solutions of □u=|u|^pwith small initial data.
• The equation u_tt − Δu = |u|^p for the critical value of p
• Biow-up of solutions of some nonlinear hyperbolic equations
• Weighted Strichartz estimates and global existence for semilinear wave equations
• Strichartz estimates in the hyperbolic space and global existence for the semilinear wave equation
• The critical exponent for a time fractional diffusion equation with nonlinear memory
• Long-time existence for small amplitude semilinear wave equations
• Life-Span of Solutions to Critical Semilinear Wave Equations