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The regularization of nonlinear electrical circuits [PDF]
Proceedings of the American Mathematical Society, 1975 Recently Smale [1] proposed the question ’under what conditions can an electrical circuit be regularized?’ This note gives a solution to the problem.
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Constant sign and nodal solutions for nonlinear Robin equations with locally defined source term
Mathematical Modelling and Analysis, 2020 We consider a parametric Robin problem driven by a nonlinear, nonhomogeneous differential operator which includes as special cases the p-Laplacian and the (p,q)-Laplacian. The source term is parametric and only locally defined (that is, in a neighborhood
Nikolaos S. Papageorgiou +2 more
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Nonlinear Eigenvalue Approach to Differential Riccati Equations for Contraction Analysis [PDF]
, 2016 In this paper, we extend the eigenvalue method of the algebraic Riccati equation to the differential Riccati equation (DRE) in contraction analysis. One of the main results is showing that solutions to the DRE can be expressed as functions of nonlinear ...
Kawano, Yu, Ohtsuka, Toshiyuki
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Solutions of Smooth Nonlinear Partial Differential Equations
Abstract and Applied Analysis, 2011 The method of order completion provides a general and type-independent theory for the existence and basic regularity of the solutions of large classes of systems of nonlinear partial differential equations (PDEs). Recently, the application of convergence
Jan Harm van der Walt
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Schaeffer's regularity theorem for scalar conservation laws does not extend to systems [PDF]
, 2017 Several regularity results hold for the Cauchy problem involving one scalar conservation law having convex flux. Among these, Schaeffer's theorem guarantees that if the initial datum is smooth and is generic, in the Baire sense, the entropy admissible ...
Caravenna, Laura, L., Spinolo
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Nonlinear Parabolic Equations with Regularized Derivatives
Journal of Mathematical Analysis and Applications, 1999 Nonlinear systems of differential equations \[ \partial_tu+\partial_xf(u)+g(u)=\Delta u\tag{1} \] are considered on \(\mathbb R_+^{n+1}\) \((t>0)\), where \(u=(u_1,\dots,u_m)^T\), \(f(u)=(f_1(u),\dots,f_n(u))^T\), \(\partial_xf(u)=\sum_{i=1}^n\partial_{x_i}f_i(u)\).
Wang, Y.G., Oberguggenberger, M.
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Fast nonlinear susceptibility inversion with variational regularization [PDF]
Magnetic Resonance in Medicine, 2018 PurposeQuantitative susceptibility mapping can be performed through the minimization of a function consisting of data fidelity and regularization terms. For data consistency, a Gaussian‐phase noise distribution is often assumed, which breaks down when the signal‐to‐noise ratio is low.
Carlos Milovic +4 more
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Tikhonov regularized iterative methods for nonlinear problems
Optimization, 2023 We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions like strong convexity or strong monotonicity on the considered operators to prove strong convergence of the ...
Avinash Dixit +3 more
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Nonlinear Eigenvalue Problems for the Dirichlet (p,2)-Laplacian
Axioms, 2022 We consider a nonlinear eigenvalue problem driven by the Dirichlet (p,2)-Laplacian. The parametric reaction is a Carathéodory function which exhibits (p−1)-sublinear growth as x→+∞ and as x→0+.
Yunru Bai +2 more
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Regularization for Nonlinear System Identification
, 2022 AbstractIn this chapter we review some basic ideas for nonlinear system identification. This is a complex area with a vast and rich literature. One reason for the richness is that very many parameterizations of the unknown system have been suggested, each with various proposed estimation methods.
Gianluigi Pillonetto +4 more
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