Well-posedness results for fractional semi-linear wave equations
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Publication:2284895
DOI10.3934/dcdsb.2019255zbMath1443.35100OpenAlexW2990877263WikidataQ126786623 ScholiaQ126786623MaRDI QIDQ2284895
Jean-Daniel Djida, Arran Fernandez, IvÁn Area
Publication date: 15 January 2020
Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdsb.2019255
Smoothness and regularity of solutions to PDEs (35B65) Initial value problems for second-order hyperbolic equations (35L15) Fractional partial differential equations (35R11) Second-order semilinear hyperbolic equations (35L71) Existence of solutions of equilibrium problems in solid mechanics (74G22)
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Cites Work
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- A parabolic problem with a fractional time derivative
- An extension problem for the fractional derivative defined by Marchaud
- Hitchhiker's guide to the fractional Sobolev spaces
- On existence and uniqueness of solutions for semilinear fractional wave equations
- Representation of solutions and large-time behavior for fully nonlocal diffusion equations
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- A fractional porous medium equation
- An introduction to Sobolev spaces and interpolation spaces
- Continuity of the temperature in boundary heat control problems
- Positive solutions of nonlinear problems involving the square root of the Laplacian
- Geometric theory of semilinear parabolic equations
- Nonlinear potential theory and weighted Sobolev spaces
- Boundary regularity for a degenerate elliptic equation with mixed boundary conditions
- A simple mathematical model inspired by the Purkinje cells: from delayed travelling waves to fractional diffusion
- Cauchy problem for fractional diffusion equations
- An elliptic regularity theorem for fractional partial differential operators
- Getting acquainted with the fractional Laplacian
- Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions
- Regularity of solutions to space-time fractional wave equations: A PDE approach
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- Well-posedness results for a class of semi-linear super-diffusive equations
- Symmetrization for linear and nonlinear fractional parabolic equations of porous medium type
- Maximum principles, extension problem and inversion for nonlocal one-sided equations
- ASYMPTOTIC BEHAVIORS OF FUNDAMENTAL SOLUTION AND ITS DERIVATIVES TO FRACTIONAL DIFFUSION-WAVE EQUATIONS
- Positive solutions of the nonlinear Schrödinger equation with the fractional Laplacian
- From the long jump random walk to the fractional Laplacian
- A General Fractional Porous Medium Equation
- Extension Problem and Harnack's Inequality for Some Fractional Operators
- Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
- Global Existence of Small Data Solutions to the Semilinear Fractional Wave Equation
- Regularity of the obstacle problem for a fractional power of the laplace operator
- Energy Inequalities for Integro-Partial Differential Equations with Riemann–Liouville Integrals
- A generalisation of the Malgrange–Ehrenpreis theorem to find fundamental solutions to fractional PDEs
- Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation, II
- An Extension Problem Related to the Fractional Laplacian
- Mittag-Leffler Functions, Related Topics and Applications
- Explicit Barenblatt profiles for fractional porous medium equations
- Weighted Norm Inequalities for the Hardy Maximal Function
- Marcinkiewicz Interpolation Theorem and Marcinkiewicz Spaces
- Space-time estimates of linear flow and application to some nonlinear integro-differential equations corresponding to fractional-order time derivative