Solutions to Non-linear Euler-Poisson-Darboux Equations by Means of Generalized Separation of Variables

Garra, Roberto; Orsingher, Enzo; Shishkina, Elina

doi:10.1134/s1995080219050093

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…9 Subsequent generalizations of such a model are presented in articles. [10][11][12][13][14] A more detailed historical overview is given in papers. 15,16 The random walk introduced by Pearson (Pearson walks) has a large number of applications.…”

Section: Introductionmentioning

confidence: 99%

Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions

Kuznetsov

Shishkina

Rataj

2022

Math Methods in App Sciences

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This study focused on simulation and analytical models of a multidimensional random walk of many agents. At each step, any agent can rotate by an arbitrary angle and continue moving in the direction selected. The analytical model used gives the probability of finding an agent in the circular area of the radius r in the given time moment. The model includes parameters that control the intensity of the walking process and the characteristics of the environment. Work on this topic mainly concerns the discrete case of a random walk. In this article, we consider the case of a random walk continuous in spatial coordinates. We obtain certain theoretical results for the analytical model with the help of the mathematical apparatus aimed at working with a generalized translation. With the help of a simulation, we reveal the meaning of the analytical model's parameters.Results can be used for modeling diffusion-like processes such as the spread of an epidemic, mechanical vibrations, forest fires, migration, and dissemination of information over a network.

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Section: Introductionmentioning

confidence: 99%

Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions

Kuznetsov

Shishkina

Rataj

2022

Math Methods in App Sciences

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“…It is well known that the regular diffusion equation propagates perturbations with infinite velocity. For this contradiction one possible answer is the telegraph equation which is "obviously hyperbolic" [33] or other telegraph-type equations like the Euler-Poisson-Darboux which can be derived from the modified Fick's (or Fourier's) law [34,35]. Another answer is the investigation of the nonlinear hyperbolic system of diffusion flux relaxation and energy conservation equations instead of the second order diffusion equation [36,37].…”

Section: Introductionmentioning

confidence: 99%

General self-similar solutions of diffusion equation and related constructions

Barna¹,

Mátyás²

2021

Preprint

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Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for different non-equilibrium systems. After summarizing the existing solutions of the regular diffusion equation, we present not so well known solution derived from three different trial functions, as a key point we present a family of solutions for the case of infinite horizon. By this we tried to make a step toward understanding the different long time decays for different diffusive systems.

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Euler–Poisson–Darboux equations and iterated fractional Brownian motions

Garra,

Orsingher

2023

Bol. Soc. Mat. Mex.

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Solutions to Non-linear Euler-Poisson-Darboux Equations by Means of Generalized Separation of Variables

Cited by 3 publications

References 7 publications

Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions

Comparison of simulation and analytical models for the distribution of a group of agents moving in random directions

General self-similar solutions of diffusion equation and related constructions

Euler–Poisson–Darboux equations and iterated fractional Brownian motions

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