A Framework for Nonlocal, Nonlinear Initial Value Problems

DOI10.1137/19M124143XzbMath1439.35534arXiv1809.10215OpenAlexW2893901959MaRDI QIDQ5110294

Moritz Kassmann, Grzegorz Karch, Miłosz Krupski

Publication date: 18 May 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.10215

zbMATH Keywords

existence of solutionsnonlinear diffusionnonlocal evolution equations

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Hyperbolic conservation laws (35L65) Fractional partial differential equations (35R11)

Related Items (2)

Homogenization of non-local nonlinear p-Laplacian equation with variable index and periodic structure ⋮ Homogenization of nonlinear nonlocal diffusion equation with periodic and stationary structure

Cites Work

• Unnamed Item
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• Nonlocal diffusion and applications
• An inhomogeneous nonlocal diffusion problem with unbounded steps
• Nonlocal filtration equations with rough kernels
• Fractional \(p\)-Laplacian evolution equations
• Uniqueness and properties of distributional solutions of nonlocal equations of porous medium type
• Optimal continuous dependence estimates for fractional degenerate parabolic equations
• Entropy solution theory for fractional degenerate convection-diffusion equations
• Barenblatt profiles for a nonlocal porous medium equation
• A fractional porous medium equation
• Nonlinear diffusion of dislocation density and self-similar solutions
• Asymptotic behaviour of the doubly nonlinear diffusion equation \(u_t=\Delta_pu^m\) on bounded domains
• Nonlinear porous medium flow with fractional potential pressure
• A Widder's type theorem for the heat equation with nonlocal diffusion
• The Cauchy problem for a one-dimensional nonlinear elastic peridynamic model
• Fractional porous media equations: existence and uniqueness of weak solutions with measure data
• Finite and infinite speed of propagation for porous medium equations with nonlocal pressure
• Functional analysis, Sobolev spaces and partial differential equations
• Compact sets in the space \(L^ p(0,T;B)\)
• On distributional solutions of local and nonlocal problems of porous medium type
• Large time behaviour of the doubly nonlinear porous medium equation
• Kato's inequality when \(\Delta u\) is a measure
• The nonlocal porous medium equation: Barenblatt profiles and other weak solutions
• Classical solutions and higher regularity for nonlinear fractional diffusion equations
• Stochastic generalized porous media and fast diffusion equations
• Asymptotic behaviour of a porous medium equation with fractional diffusion
• On the Cauchy problem for a general fractional porous medium equation with variable density
• Finite and infinite speed of propagation for porous medium equations with fractional pressure
• Well-posedness of the peridynamic model with Lipschitz continuous pairwise force function
• Schrödinger operators with singular potentials
• The Dirichlet problem for the fractional \(p\)-Laplacian evolution equation
• Fractional eigenvalues
• Diffusion and Reactions in Fractals and Disordered Systems
• A General Fractional Porous Medium Equation
• Continuous Dependence Estimates for Nonlinear Fractional Convection-diffusion Equations
• A First Course in Sobolev Spaces
• The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion
• Wellposedness of a nonlinear peridynamic model
• Infinite Speed of Propagation and Regularity of Solutions to the Fractional Porous Medium Equation in General Domains
• $L^1$ Contraction for Bounded (Nonintegrable) Solutions of Degenerate Parabolic Equations
• Fractal Hamilton-Jacobi-KPZ equations
• Measure-valued and weak solutions to the nonlinear peridynamic model in nonlocal elastodynamics

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