The Cournot duopoly game modeled by Kopel, with adaptive expectations, is generalized by introducing the self-diffusion and cross-diffusion terms. General properties, such as boundedness and uniqueness, are obtained. Non-linear stability results are reached by the analysis of the stability of a ODE system.

On the dynamics of a non-linear Duopoly game model

The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed. An asymptotic analysis is achieved proving that for large t, the in uences of the initial data vanish, while the effects of boundary disturbances are everywhere bounded.

Asymptotic estimates related to an integro differential equation

A superconductive model characterized by a third order parabolic operator $ {\mathcal L}_\varepsilon $ is analyzed. When the viscous terms, represented by higher-order derivatives, tend to zero, a hyperbolic operator $ {\mathcal L}_0 $ appears. Furthermore, if
${\mathcal P}_\varepsilon$ is the Dirichlet initial-boundary value problem for $ {\mathcal L}_\varepsilon$,
when ${\mathcal L}
_\varepsilon $ turns into ${\mathcal
L}_0 , $
 ${\mathcal P}_\varepsilon$ turns into a problem ${\mathcal P}_0$ with the same initial-boundary conditions of
${\mathcal P}_\varepsilon $.
As long as the higher-order derivatives of the solution of ${\mathcal P}_0$ are bounded, an estimate of solution for the nonlinear problem related to the remainder term $ r, $ is achieved. Moreover, some classes of explicit solutions related to $ {\mathcal P}_0 $ are determined, proving the existence of at least one motion whose derivatives are bounded. The estimate shows that the diffusion effects are bounded even when time tends to infinity.

Diffusion effects in a superconductive model

A superconductive model characterized by a third order parabolic operator L" is analysed When the viscous terms, represented by higher - order deriva- tives, tend to zero, a hyperbolic operator L0 appears Furthermore, if P" is the Dirichlet initial boundary - value problem for L", when L" turns into L0; P" turns into a problem P0 with the same initial - boundary conditions as P" The solution of the nonlinear problem related to the remainder term r is achieved, as long as the higher-order derivatives of the solution of P0 are bounded More- over, some classes of explicit solutions related to P0 are determined, proving the existence of at least one motion whose derivatives are bounded The estimate shows that the diffusion effects are bounded even when time tends to infinity

Diffusion effects on a superconductive model

A parabolic integro differential operator $\mathcal{L}$ , suitable to describe many phenomena in various physical fields, is considered By means of equivalence between $\mathcal{L}$ and the third order equation describing the evolution inside an exponentially shaped Josephson junction (ESJJ), an asymptotic analysis for (ESJJ) is achieved, explicitly evaluating, boundary contributions related to the Dirichlet problem

On Asymptotic Effects of Boundary Perturbations in Exponentially Shaped Josephson Junctions

We briefly present new results on the existence and uniqueness of solutions u of a large class of initial-boundary-value problems characterized by a quasi-linear third order equation on a finite space interval with Dirichlet, Neumann or pseudoperiodic boundary conditions. The class includes equations arising in Superconductor Theory and in the Theory of Viscoelastic Materials.

Existence and Uniqueness for Some 3rd Order Dissipative Problems with Various Boundary Conditions

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

A. D’Anna

Author Tools

Chat about Author

Papers

Existence and Uniqueness for Some 3rd Order Dissipative Problems with Various Boundary Conditions