Parabolic approximation of damped wave equations via fractional powers: fast growing nonlinearities and continuity of the dynamics
From MaRDI portal
Publication:511250
DOI10.1016/j.jmaa.2017.01.024zbMath1356.35141OpenAlexW2575384730MaRDI QIDQ511250
Jan W. Cholewa, Flank D. M. Bezerra, Alexandre Nolasco De Carvalho, Marcelo J. D. Nascimento
Publication date: 14 February 2017
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.01.024
Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Fractional partial differential equations (35R11) Second-order semilinear hyperbolic equations (35L71)
Related Items
A second-order evolution equation and logarithmic operators ⋮ Fractional oscillon equations: continuity properties of attractors with respect to order of the equations ⋮ Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations ⋮ Logarithmic counterpart for semilinear Schrödinger equations ⋮ Fractional powers approach of operators for abstract evolution equations of third order in time ⋮ Regularity and stability of wave equations with variable coefficients and Wentzell type boundary conditions ⋮ Chebyshev polynomials for higher order differential equations and fractional powers ⋮ Strong attractors and their stability for the structurally damped Kirchhoff wave equation with supercritical nonlinearity ⋮ A higher-order non-autonomous semilinear parabolic equation ⋮ Optimal convergence rates for damped inertial gradient dynamics with flat geometries ⋮ Continuity of the attractors in time-dependent spaces and applications ⋮ Fractional approximations of abstract semilinear parabolic problems ⋮ Asymptotic behaviours of solutions for wave equations with damped Wentzell boundary conditions but no interior damping ⋮ Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings ⋮ On a cascade system of Schrödinger equations. Fractional powers approach ⋮ Fractional oscillon equations; solvability and connection with classical oscillon equations ⋮ Unnamed Item ⋮ Optimal attractors of the Kirchhoff wave model with structural nonlinear damping ⋮ Strong attractors and their continuity for the semilinear wave equations with fractional damping ⋮ On spectral and fractional powers of damped wave equations
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Damped wave equations with fast growing dissipative nonlinearities
- Global attractors for wave equations with nonlinear interior damping and critical exponents
- Long-term dynamics of semilinear wave equation with nonlinear localized interior damping and a source term of critical exponent
- Extremal equilibria for monotone semigroups in ordered spaces with application to evolutionary equations
- Strongly damped wave equations in \(W^ {1,p}_ 0(\Omega)\times L^ p(\Omega)\)
- Semigroups of linear operators and applications to partial differential equations
- Regular attractors of semigroups and evolution equations
- Proof of extensions of two conjectures on structural damping for elastic systems
- Geometric theory of semilinear parabolic equations
- A remark on the damped wave equation
- Note on fractional powers of linear operators
- A damped hyerbolic equation with critical exponent
- Local well posedness for strongly damped wave equations with critical nonlinearities