Blow-up results for semi-linear structurally damped \(\sigma\)-evolution equations

DOI10.1007/978-3-030-61346-4_10zbMath1461.35070arXiv1909.01181OpenAlexW3127543424MaRDI QIDQ2662140

Tuan Anh Dao, Michael Reissig

Publication date: 9 April 2021

Full work available at URL: https://arxiv.org/abs/1909.01181

zbMATH Keywords

structural dampingtest functions\(\sigma\)-evolution equations

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Blow-up in context of PDEs (35B44) Fractional partial differential equations (35R11) Second-order semilinear hyperbolic equations (35L71)

Related Items (10)

Critical curve for a weakly coupled system of semilinear \(\sigma\)-evolution equations with frictional damping ⋮ Blowup results for the fractional Schrödinger equation without gauge invariance ⋮ Semilinear \(\sigma\)-evolution models with friction and visco-elastic type damping ⋮ Blow‐up results for a semi‐linear structural damped wave model with nonlinear memory ⋮ Note on the lifespan estimate of solutions for non-gauge invariant semilinear massless semirelativistic equations with some scaling critical nonlinearity ⋮ On asymptotic properties of solutions to \(\sigma \)-evolution equations with general double damping ⋮ Existence and nonexistence of global solutions for a wave system with different structural damping terms ⋮ Liouville-type theorems for sign-changing solutions to nonlocal elliptic inequalities and systems with variable-exponent nonlinearities ⋮ Lifespan estimates of 1D non-gauge invariant semilinear semirelativistic equations ⋮ Some nonexistence results for space-time fractional Schrödinger equations without gauge invariance

Cites Work

• Unnamed Item
• Unnamed Item
• A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations
• Ten equivalent definitions of the fractional Laplace operator
• Pseudo-differential operators, singularities, applications
• Critical regularity of nonlinearities in semilinear classical damped wave equations
• On Dirichlet's boundary value problem. An \(L^p\)-theory based on a generalization of Garding's inequality
• Semilinear structural damped waves
• Regularity of the obstacle problem for a fractional power of the laplace operator
• A note for the global nonexistence of semirelativistic equations with nongauge invariant power type nonlinearity
• On the loss of maximum principles for higher-order fractional Laplacians

This page was built for publication: Blow-up results for semi-linear structurally damped \(\sigma\)-evolution equations