Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations
DOI10.1016/j.jmaa.2021.125007zbMath1461.35215arXiv2008.10919OpenAlexW3122267609WikidataQ115345885 ScholiaQ115345885MaRDI QIDQ2660467
Patryk Wolejko, Petra Wittbold, Rico Zacher
Publication date: 30 March 2021
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2008.10919
weak solutionsubdiffusionDe Giorgi iterationfractional time derivative\( L_1\)-contractionporous medium type equation
Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) Weak solutions to PDEs (35D30) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09) Quasilinear parabolic equations (35K59)
Related Items (11)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A parabolic problem with a fractional time derivative
- Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\)
- General fractional calculus, evolution equations, and renewal processes
- Porous medium flow with both a fractional potential pressure and fractional time derivative
- Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
- An \(L_{q}(L_{p})\)-theory for the time-fractional evolution equations with variable coefficients
- Maximal regularity of type \(L_p\) for abstract parabolic Volterra equations
- Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
- Volterra integro-differential equations with accretive nonlinearity
- Compact sets in the space \(L^ p(0,T;B)\)
- An abstract nonlinear Volterra equation
- Integral equations of the first kind of Sonine type
- On a nonlinear elliptic-parabolic integro-differential equation with \(L^{1}\)-data.
- Quasilinear evolutionary equations and continuous interpolation spaces.
- Decay of solutions to parabolic-type problem with distributed order Caputo derivative
- Existence of entropy solutions to a doubly nonlinear integro-differential equation.
- Global strong solvability of a quasilinear subdiffusion problem
- Entropy solutions to doubly nonlinear integro-differential equations
- Decay estimates for evolutionary equations with fractional time-diffusion
- Fractional flows driven by subdifferentials in Hilbert spaces
- Regularity and stability analysis for a class of semilinear nonlocal differential equations in Hilbert spaces
- Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
- Stability, instability, and blowup for time fractional and other nonlocal in time semilinear subdiffusion equations
- Existence and uniqueness for parabolic problems with Caputo time derivative
- Nonlocal time porous medium equation with fractional time derivative
- Distributed order calculus and equations of ultraslow diffusion
- Lyapunov functions and convergence to steady state for differential equations of fractional order
- Completely positive measures and Feller semigroups
- Global existence for a semilinear parabolic Volterra equation
- Approximation of the Erdélyi--Kober Operator with Application to the Time-Fractional Porous Medium Equation
- Some Compactness Criteria for Weak Solutions of Time Fractional PDEs
- Asymptotic Behavior of Solutions of Nonlinear Volterra Equations with Completely Positive Kernels
- Abstract Linear and Nonlinear Volterra Equations Preserving Positivity
- Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives
- The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
- The Limiting Behavior of a One-Dimensional Random Walk in a Random Medium
- Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
- Optimal Decay Estimates for Time-Fractional and Other NonLocal Subdiffusion Equations via Energy Methods
- On heat conduction in materials with memory
- Partial differential equations. An application-oriented introduction
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
This page was built for publication: Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations