Some Compactness Criteria for Weak Solutions of Time Fractional PDEs
From MaRDI portal
Publication:3174824
DOI10.1137/17M1145549zbMath1403.35318arXiv1708.08384WikidataQ129517688 ScholiaQ129517688MaRDI QIDQ3174824
Publication date: 18 July 2018
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1708.08384
weak solutionsAubin-Lions lemmatime fractional Keller-Segel equationsweak Caputo derivativetime fractional Navier-Stokes equations
Weak solutions to PDEs (35D30) Compactness in Banach (or normed) spaces (46B50) Fractional partial differential equations (35R11)
Related Items (35)
Time-space fractional diffusion problems: existence, decay estimates and blow-up of solutions ⋮ Numerical stability of Grünwald-Letnikov method for time fractional delay differential equations ⋮ Reaction-diffusion equation based on fractional-time anisotropic diffusion for textured images recovery ⋮ Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations ⋮ Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative ⋮ A Thermo-Viscoelastic Fractional Contact Problem with Normal Compliance and Coulomb’s Friction ⋮ Global existence and asymptotic behavior of weak solutions for time-space fractional Kirchhoff-type diffusion equations ⋮ Application of capacities to space–time fractional dissipative equations I: regularity and the blow-up set ⋮ Allen-Cahn-Navier-Stokes-Voigt systems with moving contact lines ⋮ Singularity formation in fractional Burgers' equations ⋮ Well‐posedness and asymptotic behavior for the fractional Keller–Segel system in critical Besov–Herz‐type spaces ⋮ Existence of weak solutions to nonlocal PDEs with a generalized definition of Caputo derivative ⋮ Time fractional gradient flows: Theory and numerics ⋮ A linearized L1-Galerkin FEM for non-smooth solutions of Kirchhoff type quasilinear time-fractional integro-differential equation ⋮ Existence and uniqueness of weak solutions to a truncated system for a class of time-fractional reaction-diffusion-advection systems ⋮ An inverse problem of identifying the coefficient in a nonlinear time-fractional diffusion equation ⋮ Robust time‐fractional diffusion filtering for noise removal ⋮ On a class of nonlinear time‐fractional pseudo‐parabolic equations with bounded delay ⋮ Well‐posedness and blow‐up of the fractional Keller–Segel model on domains ⋮ The existence and asymptotic behavior of solutions to 3D viscous primitive equations with Caputo fractional time derivatives ⋮ Analysis of a Dilute Polymer Model with a Time-Fractional Derivative ⋮ Global weak solutions to a spatio-temporal fractional Landau-Lifshitz-Bloch equation ⋮ Unnamed Item ⋮ On an optimal control problem of time-fractional advection-diffusion equation ⋮ Global existence of solutions of the time fractional Cahn-Hilliard equation in \(\mathbb{R}^3\) ⋮ Galerkin method for time fractional semilinear equations ⋮ Non-local porous media equations with fractional time derivative ⋮ A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time-fractional derivative ⋮ A Discretization of Caputo Derivatives with Application to Time Fractional SDEs and Gradient Flows ⋮ Time-fractional Cahn-Hilliard equation: well-posedness, degeneracy, and numerical solutions ⋮ Variational time-fractional mean field games ⋮ Equivalence between a time-fractional and an integer-order gradient flow: the memory effect reflected in the energy ⋮ On existence and regularity of a terminal value problem for the time fractional diffusion equation ⋮ Delsarte equation for Caputo operator of fractional calculus ⋮ Existence, uniqueness and \(L^\infty\)-bound for weak solutions of a time fractional Keller-Segel system
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A note on \(L^\infty\)-bound and uniqueness to a degenerate Keller-Segel model
- A parabolic problem with a fractional time derivative
- Blowup of solutions to generalized Keller-Segel model
- Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos
- Uniform \(L^{\infty}\) boundedness for a degenerate parabolic-parabolic Keller-Segel model
- Representation of solutions and large-time behavior for fully nonlocal diffusion equations
- The Kolmogorov-Riesz compactness theorem
- Fractional stochastic differential equations with applications to finance
- Blow-up, zero \(\alpha\) limit and the Liouville type theorem for the Euler-poincaré equations
- Mathematical analysis II. Translated from the 4th and 6th Russian editions by Roger Cooke and Octavio T. Paniagua
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Compact sets in the space \(L^ p(0,T;B)\)
- On the concepts of state and free energy in linear viscoelasticity
- From 1970 until present: The Keller-Segel model in chemotaxis and its consequences. I
- Time fractional equations and probabilistic representation
- Fractional stochastic differential equations satisfying fluctuation-dissipation theorem
- A fractional kinetic process describing the intermediate time behaviour of cellular flows
- Ergodicity of stochastic differential equations driven by fractional Brownian motion
- Cauchy problem for fractional diffusion equations
- A note on Aubin-Lions-Dubinskiĭ lemmas
- Time-fractional diffusion equation in the fractional Sobolev spaces
- Hardy spaces on Ahlfors-regular quasi metric spaces. A sharp theory
- An introduction to Navier-Stokes equation and oceanography.
- Regularization of differential equations by fractional noise.
- Maximum principles, extension problem and inversion for nonlocal one-sided equations
- ASYMPTOTIC BEHAVIORS OF FUNDAMENTAL SOLUTION AND ITS DERIVATIVES TO FRACTIONAL DIFFUSION-WAVE EQUATIONS
- Foundations of Linear Viscoelasticity
- Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels
- Evolutionary Integral Equations and Applications
- A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs
- A note on deconvolution with completely monotone sequences and discrete fractional calculus
- Well-posedness of Hamilton–Jacobi equations with Caputo’s time fractional derivative
- Well-posedness and regularity of the Cauchy problem for nonlinear fractional in time and space equations
- Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
- Fourier Analysis and Hausdorff Dimension
- Analysis of fractional differential equations
This page was built for publication: Some Compactness Criteria for Weak Solutions of Time Fractional PDEs