Search results for "partial differential equation"
showing 10 items of 326 documents
On the a posteriori error analysis for linear Fokker-Planck models in convection-dominated diffusion problems
2018
This work is aimed at the derivation of reliable and efficient a posteriori error estimates for convection-dominated diffusion problems motivated by a linear Fokker-Planck problem appearing in computational neuroscience. We obtain computable error bounds of the functional type for the static and time-dependent case and for different boundary conditions (mixed and pure Neumann boundary conditions). Finally, we present a set of various numerical examples including discussions on mesh adaptivity and space-time discretisation. The numerical results confirm the reliability and efficiency of the error estimates derived.
Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy)
2020
The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from …
Modeling the Spatial Distribution of Xylella fastidiosa: A Nonstationary Approach with Dispersal Barriers
2022
Spatial species distribution models often assume isotropy and stationarity, implying that spatial dependence is direction-invariant and uniform throughout the study area. However, these assumptions are violated when dispersal barriers are present. Despite this, the issue of nonstationarity has been little explored in the context of plant health. The objective of this study was to evaluate the influence of barriers in the distribution of Xylella fastidiosa in the demarcated area in Alicante, Spain. Occurrence data from 2018 were analyzed through spatial Bayesian hierarchical models. The stationary model, illustrating a scenario without control interventions or geographical features, was com…
Exact constants in Poincaré type inequalities for functions with zero mean boundary traces
2014
In this paper, we investigate Poincare type inequalities for the functions having zero mean value on the whole boundary of a Lipschitz domain or on a measurable part of the boundary. We find exact and easily computable constants in these inequalities for some basic domains (rectangles, cubes, and right triangles) and discuss applications of the inequalities to quantitative analysis of partial differential equations. Copyright © 2014 John Wiley & Sons, Ltd.
Propagation d'informations le long d'une ligne de transmission non linéaire structurée en super réseau et simulant un neurone myélinisé
2019
Non-linear systems are almostly described by partial differential equations that characterize them. We have some systems such as the chain of coupled pebdelums, the protein chain comprising molecules with hydrogen bonds, atomic lattice, and so on .These systems are most often characterized by anharmonic inter particulate interactions and and then immersed in deformable potential substrates. In addition to nonlinearity and dispersion, these other phenomena namely anharmonicity and deformability are responsible for certain properties of propagation of solitary waves such as (compactons, kinks and anti-kinks, peackons, ...etc) and also the ability of the systems to transmit a signal . We used …
Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media
2011
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
Parabolic equations with nonlinear singularities
2011
Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…
Reproducing pairs of measurable functions
2017
We analyze the notion of reproducing pair of weakly measurable functions, which generalizes that of continuous frame. We show, in particular, that each reproducing pair generates two Hilbert spaces, conjugate dual to each other. Several examples, both discrete and continuous, are presented.
Systematic derivation of partial differential equations for second order boundary value problems
2022
Software systems designed to solve second order boundary value problems are typically restricted to hardwired lists of partial differential equations. In order to come up with more flexible systems, we introduce a systematic approach to find partial differential equations that result in eligible boundary value problems. This enables one to construct and combine one's own partial differential equations instead of choosing those from a pre-given list. This expands significantly end users possibilities to employ boundary value problems in modeling. To introduce the main ideas we employ differential geometry to examine the mathematical structure involved in second order boundary value problems …