Time-fractional Cahn-Hilliard equation: well-posedness, degeneracy, and numerical solutions
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Publication:2074104
DOI10.1016/j.camwa.2022.01.002OpenAlexW3148329882MaRDI QIDQ2074104
Marvin Fritz, Mabel L. Rajendran, Barbara I. Wohlmuth
Publication date: 4 February 2022
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2104.03096
weak solutionswell-posednessCahn-Hilliard equationdegenerate mobilityfractional chain inequalitytime-fractional PDE
Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional partial differential equations (35R11)
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Cites Work
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- Decay estimates for time-fractional and other non-local in time subdiffusion equations in \(\mathbb R^d\)
- Global dynamics of boundary droplets
- The Cahn-Hilliard equation with logarithmic potentials
- A conserved phase field system with memory and relaxed chemical potential
- A generalized Gronwall inequality and its application to a fractional differential equation
- Boundedness of weak solutions to evolutionary partial integro-differential equations with discontinuous coefficients
- Fractal analysis and tumour growth
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
- Volterra integro-differential equations with accretive nonlinearity
- Compact sets in the space \(L^ p(0,T;B)\)
- Convolution quadrature and discretized operational calculus. I
- A phase field system with memory: Global existence
- Optimal control of treatment time in a diffuse interface model of tumor growth
- Galerkin method for time fractional diffusion equations
- Time fractional diffusion: A discrete random walk approach
- Linking anisotropic sharp and diffuse surface motion laws via gradient flows
- Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance
- Global strong solvability of a quasilinear subdiffusion problem
- An implicit difference scheme for the time-fractional Cahn-Hilliard equations
- Galerkin method for time fractional semilinear equations
- Equivalence between a time-fractional and an integer-order gradient flow: the memory effect reflected in the energy
- A non-uniform time-stepping convex splitting scheme for the time-fractional Cahn-Hilliard equation
- On chain rule for fractional derivatives
- Time-fractional Allen-Cahn and Cahn-Hilliard phase-field models and their numerical investigation
- On power law scaling dynamics for time-fractional phase field models during coarsening
- Adaptive linear second-order energy stable schemes for time-fractional Allen-Cahn equation with volume constraint
- Time-fractional Allen-Cahn equations: analysis and numerical methods
- Numerical approximation of the Cahn-Hillard equation with memory effects in the dynamics of phase separation
- Well-posedness and long-time behaviour for the non-isothermal Cahn-Hilliard equation with memory
- A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation
- Fractional thermoelasticity
- On an incompressible Navier-Stokes/Cahn-Hilliard system with degenerate mobility
- Maximal regularity and global well-posedness for a phase field system with memory
- Lyapunov functions and convergence to steady state for differential equations of fractional order
- Attractors for the Cahn-Hilliard equation with memory in 2D
- Bounded weak solutions of time-fractional porous medium type and more general nonlinear and degenerate evolutionary integro-differential equations
- Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation
- Phase Field Equations with Memory: The Hyperbolic Case
- Decoupled, Energy Stable Schemes for Phase-Field Models of Two-Phase Incompressible Flows
- Differintegral interpolation from a bandlimited signal's samples
- On the Appearance of the Fractional Derivative in the Behavior of Real Materials
- Some Compactness Criteria for Weak Solutions of Time Fractional PDEs
- Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
- Cahn–Hilliard Inpainting and a Generalization for Grayvalue Images
- On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional
- Nonlocal reaction—diffusion equations and nucleation
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- On a Fourth-Order Degenerate Parabolic Equation: Global Entropy Estimates, Existence, and Qualitative Behavior of Solutions
- A Generalized Definition of Caputo Derivatives and Its Application to Fractional ODEs
- Well-posedness of a Cahn–Hilliard system modelling tumour growth with chemotaxis and active transport
- On the Cahn–Hilliard Equation with Degenerate Mobility
- Local and nonlocal phase-field models of tumor growth and invasion due to ECM degradation
- On the unsteady Darcy–Forchheimer–Brinkman equation in local and nonlocal tumor growth models
- The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential
- Numerical analysis of finite element method for time‐fractional Cahn‐Hilliard‐Cook equation
- On a subdiffusive tumour growth model with fractional time derivative
- Weak Solutions of Abstract Evolutionary Integro-Differential Equations in Hilbert Spaces
- On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Mathematical Methods in Continuum Mechanics of Solids
- Memory relaxation of first order evolution equations
- Some Advances on Image Processing by Means of Fractional Calculus
- Nonlinear partial differential equations with applications
- Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates
- Weak solutions for the Cahn-Hilliard equation with degenerate mobility
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