Fourier spectral methods for fractional-in-space reaction-diffusion equations [PDF]
, 2012 Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity.
Bueno-Orovio, A., Burrage, K., Kay, D.
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Asymptotics of conduction velocity restitution in models of electrical excitation in the heart [PDF]
, 2010 We extend a non-Tikhonov asymptotic embedding, proposed earlier, for calculation of conduction velocity restitution curves in ionic models of cardiac excitability.
Biktashev, V.N., Simitev, R.D.
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Method of lines transpose: High order L-stable O(N) schemes for parabolic equations using successive convolution [PDF]
, 2016 We present a new solver for nonlinear parabolic problems that is L-stable and achieves high order accuracy in space and time. The solver is built by first constructing a single-dimensional heat equation solver that uses fast O(N) convolution.
Causley, Matthew F. +3 more
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Higher order functional boundary value problems without monotone assumptions [PDF]
, 2013 In this paper, given a L1-Carathéodory function f, it is a considered the functional higher order equation, together with nonlinear functional boundary conditions, for.
Fialho, João, Minhós, Feliz
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THE ROLE OF LOWER AND UPPER SOLUTIONS IN THE GENERALIZATION OF LIDSTONE PROBLEMS [PDF]
, 2012 In this the authors consider a nonlinear fourth order fully equation coupled with the Lidstone boundary conditions, We discuss how di erent de nitions of lower and upper solutions can generalize existence and location results for boundary value problems ...
Fialho, João, Minhós, Feliz
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Space-time fractional reaction-diffusion equations associated with a generalized Riemann-Liouville fractional derivative [PDF]
, 2014 This paper deals with the investigation of the computational solutions of an unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann-
Haubold, H. J. +2 more
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Mean field limit for disordered diffusions with singular interactions
, 2014 Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and with spatial ...
Luçon, Eric, Stannat, Wilhelm
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Existence of solution for functional coupled systems with full nonlinear terms and applications to coupled a mass-spring model [PDF]
, 2017 In this paper we consider some boundary value problems composed by coupled systems of second order differential equations with full nonlinearities and general functional boundary conditions verifying some monotone assumptions.
de Sousa, Robert, Minhós, Feliz
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Existence and multiplicity of solutions in fourth order BVPs with unbounded nonlinearities [PDF]
, 2013 In this work the authors present some existence, non-existence and location results of the problem composed of a fourth order fully nonlinear equation with a parameter.In this work it is applied an Ambrosetti-Prodi type approach, with some new features ...
Fialho, João, Minhós, Feliz
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Existence of solutions to infinite elastic beam equations with unbounded nonlinearities
Electronic Journal of Differential Equations, 2017 This article concerns the existence of unbounded solutions to fourth-order boundary-value problem on the half-line with two-point boundary conditions. One-sided Nagumo condition plays a special role as it allows an asymmetric unbounded behavior on the
Hugo Carrasco, Feliz Minhos
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