Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups
From MaRDI portal
Publication:1669807
DOI10.1016/j.jde.2018.06.033zbMath1421.35224arXiv1703.07902OpenAlexW2962698001MaRDI QIDQ1669807
N. E. Tokmagambetov, Michael Ruzhansky
Publication date: 4 September 2018
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1703.07902
Analysis on real and complex Lie groups (22E30) Initial value problems for second-order hyperbolic equations (35L15) Hyperbolic equations on manifolds (58J45) Higher-order nonlinear hyperbolic equations (35L75) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Second-order semilinear hyperbolic equations (35L71)
Related Items
Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications ⋮ A comparison principle for nonlinear heat Rockland operators on graded groups ⋮ Estimates for the linear viscoelastic damped wave equation on the Heisenberg group ⋮ A global existence result for a semilinear wave equation with lower order terms on compact Lie groups ⋮ Nonlinear fractional damped wave equation on compact Lie groups ⋮ Nonexistence of solutions to higher order evolution inequalities with nonlocal source term on Riemannian manifolds ⋮ Blow-up solutions of damped Klein-Gordon equation on the Heisenberg group ⋮ Decay estimates for the linear damped wave equation on the Heisenberg group ⋮ Nonexistence results for the hyperbolic-type equations on graded Lie groups ⋮ Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity ⋮ Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations ⋮ Blow-up of solutions of nonlinear heat equation with hypoelliptic operators on graded Lie groups ⋮ Bitsadze–Samarskii type problem for the integro-differential diffusion–wave equation on the Heisenberg group ⋮ Inverse source problems for positive operators. I. Hypoelliptic diffusion and subdiffusion equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Quantization on nilpotent Lie groups
- Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups
- Sharp \(L^p\) bounds for the wave equation on groups of Heisenberg type
- Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups
- Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
- On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and \(p\)-sub-Laplacian inequalities on stratified groups
- Isoperimetric inequalities for the logarithmic potential operator
- Analysis on nilpotent groups
- \(L^p\)-estimates for the wave equation on the Heisenberg group
- Subelliptic estimates and function spaces on nilpotent Lie groups
- On a very weak solution of the wave equation for a Hamiltonian in a singular electromagnetic field
- Convolution, Fourier analysis, and distributions generated by Riesz bases
- Wave equation for operators with discrete spectrum and irregular propagation speed
- On convolutions in Hilbert spaces
- Strichartz inequalities for the wave equation with the full Laplacian on H-type groups
- The best constant problem in the Sobolev embedding theorem for complete Riemannian manifolds
- Attractors met \(X\)-elliptic operators
- Wave equation for sums of squares on compact Lie groups
- Global attractor for degenerate damped hyperbolic equations
- Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary
- A pseudo-differential calculus on the Heisenberg group
- Phase-space analysis and pseudodifferential calculus on the Heisenberg group
- Minimum Eigenvalues for Positive, Rockland Operators
- Caracterisation des operateurs hypoelliptiques homogenes
- Parametrices for hypoelliptic operators on step to nilpotent lie groups
- Harmonic Analysis in Phase Space. (AM-122)
- Hypoellipticity on the Heisenberg Group-Representation-Theoretic Criteria
- Sobolev spaces on graded Lie groups
- Nonharmonic Analysis of Boundary Value Problems
- Nonharmonic Analysis of Boundary Value Problems Without WZ Condition
- Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
- A Class of Sub-elliptic Equations on the Heisenberg Group and Related Interpolation Inequalities
- A Pseudo-differential Calculus on Graded Nilpotent Lie Groups
- Strichartz Inequalities for the Wave Equation with the Full Laplacian on the Heisenberg Group
- Besov spaces and Strichartz estimates on the Heisenberg group
