Search results for "Nonlinear"

A rescaling algorithm for the numerical solution to the porous medium equation in a two-component domain

2016

Abstract The aim of this paper is to design a rescaling algorithm for the numerical solution to the system of two porous medium equations defined on two different components of the real line, that are connected by the nonlinear contact condition. The algorithm is based on the self-similarity of solutions on different scales and it presents a space-time adaptable method producing more exact numerical solution in the area of the interface between the components, whereas the number of grid points stays fixed.

Active macro-zone approach for incremental elastoplastic-contact analysis

2013

SUMMARY The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem. A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) betw…

Corrigendum to “Fractional differential equations solved by using Mellin transform” [Commun Nonlinear Sci Numer Simul 19(7) (2014) 2220–2227]

2015

Implicit analytic solutions for a nonlinear fractional partial differential beam equation

2020

Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and u…

Efficient numerical method for simulating static and dynamic properties of superfluid helium

2004

Density functional theory (DFT) offers computationally affordable way of describing static and dynamic properties of superfluid 4He. In general, the DFT models yield single particle-like Schrodinger equations with a nonlinear potential term that accounts for all the many-body interactions. The resulting equations can be solved for small amplitude plane wave excitations in the bulk whereas fully numerical solution must be sought in more complicated cases. In this paper we propose a numerical method that can be used in solving the time-dependent nonlinear Schrodinger equation in both real and imaginary times. The method is based on operator splitting technique where each component operator is…

Partial differential equations governed by accretive operators

2012

The theory of nonlinear semigroups in Banach spaces generated by accretive operators has been very useful in the study of many nonlinear partial differential equations Such a theory is fundamentally based in the Crandall-Liggett Theorem and in the contributions of Ph. Benilan. In this paper, after outlining some of the main points of this theory, we present some of the applications to some nonlinear partial differential equations that appear in different fields of Science.

Nonlinear concave-convex problems with indefinite weight

2021

We consider a parametric nonlinear Robin problem driven by the p-Laplacian and with a reaction having the competing effects of two terms. One is a parametric (Formula presented.) -sublinear term (concave nonlinearity) and the other is a (Formula presented.) -superlinear term (convex nonlinearity). We assume that the weight of the concave term is indefinite (that is, sign-changing). Using the Nehari method, we show that for all small values of the parameter (Formula presented.), the problem has at least two positive solutions and also we provide information about their regularity.

A velocity–diffusion method for a Lotka–Volterra system with nonlinear cross and self-diffusion

2009

The aim of this paper is to introduce a deterministic particle method for the solution of two strongly coupled reaction-diffusion equations. In these equations the diffusion is nonlinear because we consider the cross and self-diffusion effects. The reaction terms on which we focus are of the Lotka-Volterra type. Our treatment of the diffusion terms is a generalization of the idea, introduced in [P. Degond, F.-J. Mustieles, A deterministic approximation of diffusion equations using particles, SIAM J. Sci. Stat. Comput. 11 (1990) 293-310] for the linear diffusion, of interpreting Fick's law in a deterministic way as a prescription on the particle velocity. Time discretization is based on the …

Supratransmission-induced traveling breathers in long Josephson junctions

2022

The emergence of travelling sine-Gordon breathers due to the nonlinear supratransmission effect is theoretically studied in a long Josephson junction driven by suitable magnetic pulses, taking into account the presence of dissipation, a current bias, and a thermal noise source. The simulations clearly indicate that, depending on the pulse's shape and the values of the main system parameters, such a configuration can effectively yield breather excitations only. Furthermore, a nonmonotonic behavior of the breather-only generation probability is observed as a function of the noise intensity. Finally, the dynamics of the supratransmission-induced breathers is characterized by looking at quantit…

Nonlinear FE analysis of out-of-plane behaviour of masonry walls with and without CFRP reinforcement

2014

Abstract The out-of-plane behaviour of unreinforced and CFRP reinforced masonry wall is studied by means of experimental investigation and numerical FE modelling. The latter is based on a linear constitutive law both for ashlars and mortar joints constituting masonry and the lines of potential delamination are taken into account by means of an interface element with bi-linear law, reproducing the opening failure mode. When reinforcement is introduced, an interface element with bi-linear law is also used, reproducing sliding failure mode. Comparison between numerical and experimental results show the reliability of the modelling. Moreover, a parametric analysis is carried out in order to inv…