Results 21 to 30 of about 36,953 (196)
Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain $ $ of $G$ of the form $$ u_t^ (x,t)=\int_{G}\frac{1}{ ^2}K_ (x,y)(u^ (y,t)-u^ (x,t))\,dy, \qquad x\in $$ with $u^ =g(x,t)$ for $x\notin $. For appropriate rescaled kernel $K_ $ we prove that solutions $u^ $, when $ \rightarrow0$, uniformly approximate the ...
Isolda E. Cardoso, Raúl E. Vidal
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Nonlocal Diffusion and Applications [PDF]
, 2016 Working in the fractional Laplace framework, this book provides models and theorems related to nonlocal diffusion phenomena. In addition to a simple probabilistic interpretation, some applications to water waves, crystal dislocations, nonlocal phase transitions, nonlocal minimal surfaces and Schrödinger equations are given.
Bucur, Claudia and Valdinoci, Enrico
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Effective nonlocal kernels on reaction–diffusion networks
Journal of Theoretical Biology, 2021 A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel"
Shin-Ichiro Ei +4 more
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A local/nonlocal diffusion model [PDF]
Applicable Analysis, 2021 In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the gradient flow of an energy functional.
Santos, Bruna C. dos +2 more
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Biological modeling with nonlocal advection–diffusion equations
Mathematical Models and Methods in Applied Sciences, 2023 The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as cell adhesion, critical to the development and structure of tissues.
Painter, K.J., Hillen, T., Potts, J.R.
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Isoperimetric inequalities in nonlocal diffusion problems with integrable kernel [PDF]
Opuscula MathematicaWe deduce isoperimetric estimates for solutions of linear stationary and evolution problems. Our main result establishes the comparison in norm between the solution of a problem and its symmetric version when nonlocal diffusion defined through integrable
Gonzalo Galiano
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Journal of Mathematical Analysis and Applications, 2015 In this paper, the authors are concerned with the existence of solutions to nonlocal parabolic partial differential equations, in the sense of aiming to construct solutions that inherit a certain minimizing property. Such parabolic minimizers or variational solutions are advantageous since they are likely to possess better regularity properties due to ...
Bögelein, Verena +3 more
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Dynamics of a nonlocal SIR epidemic model with free boundaries
Franklin Open, 2023 This paper is devoted to a nonlocal SIR type epidemic model, with free boundary denoting the expanding front. We aim to examine the full information about the dynamical behaviors of the involved disease that caused by the nonlocal diffusion and growing ...
Jia-Feng Cao +3 more
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A nonlocal convection–diffusion equation
Journal of Functional Analysis, 2007 The authors study a nonlocal equation of the form \(u_t = J*u -u + G*(f(u)) - f(u)\) in \((0,\infty)\times\mathbb R^d\) subject to the initial condition \(u(x,0) = u_0(x)\), \(x \in\mathbb R^d\), with \(J\) radially symmetric and \(G\) not necessary symmetric. The nonlinearity \(f\) is assumed to be nondecreasing with \(f(0) = 0\) and locally Lipschitz
Ignat, L.I., Rossi, J.D.
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A Strong Maximum Principle for Nonlinear Nonlocal Diffusion Equations
Axioms, 2023 We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle
Tucker Hartland, Ravi Shankar
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