Results 81 to 90 of about 280,466 (259)
Assessment of Gibbs Free Energy Calculation in PI‐Controlled Heating
Chemie Ingenieur Technik, EarlyView.For description and control of chemical processes in lab or industry thermodynamic variable Gibbs free energy provides opportunity to compare and interpret phenomena, even on a quantitative level. In a case study for PI‐controlled heating, impacts on its limits from control delay until parameter quantization are highlighted and assessed.
Jannik Dutschke +4 more
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A pointwise inequality for fractional laplacians
Advances in Mathematics, 2015 The fractional laplacian is an operator appearing in several evolution models where diffusion coming from a Lévy process is present but also in the analysis of fluid interphases. We provide an extension of a pointwise inequality that plays a rôle in their study. We begin recalling two scenarios where it has been used.
Cordoba Barba, Antonio +1 more
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Numerical approximation of the integral fractional Laplacian [PDF]
Numerische Mathematik, 2019 We propose a new nonconforming finite element algorithm to approximate the solution to the elliptic problem involving the fractional Laplacian. We first derive an integral representation of the bilinear form corresponding to the variational problem. The numerical approximation of the action of the corresponding stiffness matrix consists of three steps:
Andrea Bonito +2 more
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On the Solvability of Caputo -Fractional Boundary Value Problem Involving -Laplacian Operator
Abstract and Applied Analysis, 2013 We consider the model of a Caputo -fractional boundary value problem involving -Laplacian operator. By using the Banach contraction mapping principle, we prove that, under some conditions, the suggested model of the Caputo -fractional boundary value ...
Hüseyin Aktuğlu, Mehmet Ali Özarslan
doaj +1 more source
Immersed Boundary Projection Method for Boundaries With Slip Velocities
International Journal for Numerical Methods in Fluids, EarlyView.A formulation of the immersed boundary method for incompressible flow over arbitrarily‐shaped bodies with surface slip described by the Navier boundary condition is presented. The wall slip velocity and the boundary force are determined implicitly through a projection to satisfy both the boundary condition and the divergence‐free condition of the ...
Takehiro Fujii, Takeshi Omori
wiley +1 more source
Numerical Homogenization of Heterogeneous Fractional Laplacians [PDF]
Multiscale Modeling & Simulation, 2018 In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs. Moreover, the fractional Laplacian is a nonlocal operator in its standard form, however the Caffarelli-Silvestre extension allows for a ...
Donald L. Brown +2 more
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On comparison of fractional Laplacians [PDF]
Nonlinear Analysis, 2022 For $s>-1$, $s\notin\mathbb N_0$, we compare two natural types of fractional Laplacians $(-Δ)^s$, namely, the restricted Dirichlet and the spectral Neumann ones. We show that for the quadratic form of their difference taken on the space $\tilde{H}^s(Ω)$ is positive or negative depending on whether the integer part of $s$ is even or odd.
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Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The present work is devoted to establishing existence results and examining the stability properties of solutions associated with a generalized Brusselator reaction–diffusion system in both the classical and fractional‐order settings. The corresponding ODE and PDE formulations are considered to establish the global existence of solutions in ...
Fadia Haouam +3 more
wiley +1 more source
Non-Nehari Manifold Method for Fractional p-Laplacian Equation with a Sign-Changing Nonlinearity
Journal of Function Spaces, 2018 We consider the following fractional p-Laplacian equation: -Δpαu+V(x)up-2u=f(x,u)-Γ(x)uq-2u, x∈RN, where N≥2, pα⁎>q>p≥2, α∈(0,1), -Δpα is the fractional p-Laplacian, and Γ∈L∞(RN) and Γ(x)≥0 for a.e. x∈RN. f has the subcritical growth but higher than Γ(x)
Huxiao Luo, Shengjun Li, Wenfeng He
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Optimal control of fractional systems: a diffusive formulation [PDF]
, 2010 Optimal control of fractional linear systems on a finite horizon can be classically formulated using the adjoint system. But the adjoint of a causal fractional integral or derivative operator happens to be an anti-causal operator: hence, the adjoint ...
Matignon, Denis
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