Search results for "Differential equation"
showing 10 items of 759 documents
Exact treatment of linear difference equations with noncommutative coefficients
2007
The exact solution of a Cauchy problem related to a linear second-order difference equation with constant noncommutative coefficients is reported.
Exact treatment of operator difference equations with nonconstant and noncommutative coefficients
2013
We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.
Theoretical study on travelling web dynamics and instability under non-homogeneous tension
2013
Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibration…
How diffusivity, thermocline and incident light intensity modulate the dynamics of Deep Chlorophyll Maximum in Tyrrhenian Sea
2015
During the last few years theoretical works have shed new light and proposed new hypotheses on the mechanisms which regulate the spatio-temporal behaviour of phytoplankton communities in marine pelagic ecosystems. Despite this, relevant physical and biological issues, such as effects of the time- dependent mixing in the upper layer, competition between groups, and dynamics of non-stationary deep chlorophyll maxima, are still open questions. In this work, we analyze the spatio-temporal behaviour of five phytoplankton populations in a real marine ecosystem by using a one-dimensional reaction-diffusion-taxis model. The study is performed, taking into account the seasonal variations of environm…
Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data
2017
AbstractField data on chlorophyll distribution are investigated in a two-dimensional spatial domain of the Mediterranean Sea by using for phytoplankton abundances an advection-diffusion-reaction model, which includes real values for physical and biological variables. The study exploits indeed hydrological and nutrients data acquired in situ, and includes intraspecific competition for limiting factors, i.e. light intensity and phosphate concentration. As a result, the model allows to analyze how both the velocity field of marine currents and the two components of turbulent diffusivity affect the spatial distributions of phytoplankton abundances in the Modified Atlantic Water, the upper layer…
Dynamics of Two Picophytoplankton Groups in Mediterranean Sea: Analysis of the Deep Chlorophyll Maximum by a Stochastic Advection-Reaction-Diffusion …
2013
A stochastic advection-reaction-diffusion model with terms of multiplicative white Gaussian noise, valid for weakly mixed waters, is studied to obtain the vertical stationary spatial distributions of two groups of picophytoplankton, i.e., picoeukaryotes and Prochlorococcus, which account about for 60% of total chlorophyll on average in Mediterranean Sea. By numerically solving the equations of the model, we analyze the one-dimensional spatio-temporal dynamics of the total picophytoplankton biomass and nutrient concentration along the water column at different depths. In particular, we integrate the equations over a time interval long enough, obtaining the steady spatial distributions for th…
Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/143614 Open Access We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.
Asymptotic Behavior of Higher-Order Quasilinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/395368 Open Access We study asymptotic behavior of solutions to a class of higher-order quasilinear neutral differential equations under the assumptions that allow applications to even- and odd-order differential equations with delayed and advanced arguments, as well as to functional differential equations with more complex arguments that may, for instance, alternate indefinitely between delayed and advanced types. New theorems extend a number of results reported in the literature. Illustrative examples are presented.
Systematisation of Systems Solving Physics Boundary Value Problems
2020
A general conservation law that defines a class of physical field theories is constructed. First, the notion of a general field is introduced as a formal sum of differential forms on a Minkowski manifold. By the action principle the conservation law is defined for such a general field. By construction, particular field notions of physics, e.g., magnetic flux, electric field strength, stress, strain etc. become instances of the general field. Hence, the differential equations that constitute physical field theories become also instances of the general conservation law. The general field and the general conservation law together correspond to a large class of relativistic hyperbolic physical …
Oscillation of fourth-order quasilinear differential equations
2015
We study oscillatory behavior of a class of fourth-order quasilinear differential equations without imposing restrictive conditions on the deviated argument. This allows applications to functional differential equations with delayed and advanced arguments, and not only these. New theorems are based on a thorough analysis of possible behavior of nonoscillatory solutions; they complement and improve a number of results reported in the literature. Three illustrative examples are presented.