Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and \(C^0\) potentials on arbitrary bounded domains

DOI10.1216/RMJ-2019-49-4-1307zbMath1437.35503OpenAlexW2971300614MaRDI QIDQ2323930

Joseph L. Shomberg

Publication date: 13 September 2019

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1567044041

zbMATH Keywords

regularityuniquenessweak solutionsmild solutionsglobal well-posednessnonlocal diffusion

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Long-time behavior of solutions for dynamical problems in solid mechanics (74H40) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11) Second-order semilinear hyperbolic equations (35L71)

Related Items (3)

Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain ⋮ Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation ⋮ Global existence and dynamic structure of solutions for damped wave equation involving the fractional Laplacian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence, uniqueness and asymptotic behaviour for fractional porous medium equations on bounded domains
• Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions
• On the strong-to-strong interaction case for doubly nonlocal Cahn-Hilliard equations
• Semigroups of linear operators and applications to partial differential equations
• Censored stable processes
• Global attractors for damped semilinear wave equations.
• On the strongly damped wave equation
• Attractors for strongly damped wave equations with critical nonlinearities.
• Analyticity and regularity for a class of second order evolution equations
• Analyticity and Gevrey class regularity for a strongly damped wave equation with hyperbolic dynamic boundary conditions
• The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets
• Recent progress in the theory of nonlinear diffusion with fractional Laplacian operators
• Quantitative local and global a priori estimates for fractional nonlinear diffusion equations
• Fractional Cahn-Hilliard, Allen-Cahn and porous medium equations
• Smooth attractors for strongly damped wave equations
• Mechanical Behavior of Materials
• Shorter Notes: Strongly Continuous Semigroups, Weak Solutions, and the Variation of Constants Formula
• Local well posedness for strongly damped wave equations with critical nonlinearities
• An Introduction to Partial Differential Equations
• Gevrey Class Semigroups Arising from Elastic Systems with Gentle Dissipation: The Case 0 < α < ½

This page was built for publication: Well-posedness of semilinear strongly damped wave equations with fractional diffusion operators and \(C^0\) potentials on arbitrary bounded domains