Blow-up results for viscoelastic wave equations with damping terms on stratified groups
DOI10.1007/s40840-022-01308-xOpenAlexW4281479981MaRDI QIDQ2082403
Ardak Kashkynbayev, Aidyn Kassymov, Durvudkhan Suragan
Publication date: 4 October 2022
Published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40840-022-01308-x
Sobolev inequalitysub-LaplacianHeisenberg groupsviscoelastic wave equationGreen's identitystratified groupsPoincáre inequality
Initial-boundary value problems for second-order hyperbolic equations (35L20) Analysis on real and complex Lie groups (22E30) Analysis on other specific Lie groups (43A80) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Blow-up in context of PDEs (35B44) Integro-partial differential equations (35R09) Second-order semilinear hyperbolic equations (35L71)
Cites Work
- Quantization on nilpotent Lie groups
- Blow up in a nonlinear viscoelastic wave equation with strong damping
- Global nonexistence of positive initial energy solutions for a viscoelastic wave equation
- On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and \(p\)-sub-Laplacian inequalities on stratified groups
- Green's identities, comparison principle and uniqueness of positive solutions for nonlinear \(p\)-sub-Laplacian equations on stratified Lie groups
- A blow-up result in a Cauchy viscoelastic problem
- Subelliptic estimates and function spaces on nilpotent Lie groups
- Existence of a solution of the wave equation with nonlinear damping and source terms
- Global nonexistence theorems for quasilinear evolution equations with dissipation
- Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups.
- Global nonexistence theorems for a class of evolution equations with dissipation
- Blow-up of solutions of nonlinear heat equation with hypoelliptic operators on graded Lie groups
- Nonexistence results for the hyperbolic-type equations on graded Lie groups
- Hardy inequalities on homogeneous groups. 100 years of Hardy inequalities
- Existence and decay of solutions of a viscoelastic equation with a nonlinear source
- Global solutions and finite time blow up for damped semilinear wave equations
- Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation
- Hypoelliptic second order differential equations
- Stratified Lie Groups and Potential Theory for their Sub-Laplacians
- Blow up and global existence in a nonlinear viscoelastic wave equation
- Asymptotic Stability and Energy Decay Rates for Solutions of the Wave Equation with Memory in a Star-Shaped Domain
- Lower bounds for the blow-up time to a nonlinear viscoelastic wave equation with strong damping