Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations

Barna, Imre Ferenc; Mátyás, László

doi:10.3390/math10183281

Cited by 9 publications

(12 citation statements)

References 85 publications

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“…The present study organically follows our former analysis in which we in-depth investigated the regular diffusion equation [14][15][16]. Now we extend our research to the complex diffusion processes which is formally equivalent to the free Schrödinger equation.…”

Section: Of 15mentioning

confidence: 76%

“…An exhaustive analysis of Eq. ( 5) was done in our previous studies [14][15][16] which we skip here.…”

Section: Cartesian Casementioning

confidence: 99%

“…Additional variable reduction Ansätze (which describes non-classical symmetries) are available too [15] and will be tested to these equations. Conflicts of Interest: The authors declare no conflict of interest.…”

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confidence: 99%

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Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Barna,

Mátyás

2023

Preprint

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In our latest studies with the help of the self-similar Ansatz we derived new type of 1 solutions for the regular diffusion equation which are much more complex than the well-known 2 Gaussian and error functions. These solutions contain additional Kummer’s M and Kummer’s U 3 functions with quadratic argument. In the present treaties we perform an analogous analysis for the 4 regular diffusion equation which has a complex diffusion coefficient. Formally, it is equivalent to 5 the free Schrödinger equation however it is far from being trivial how the solutions can be given 6 quantum mechanical interpretation. We investigate both the one dimensional Cartesian and the 7 spherical symmetric equations. We find solutions which fulfill the L2 integrability criteria therefore 8 might have quantum mechanical relevance in the future.

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Section: Of 15mentioning

confidence: 76%

“…An exhaustive analysis of Eq. ( 5) was done in our previous studies [14][15][16] which we skip here.…”

Section: Cartesian Casementioning

confidence: 99%

See 1 more Smart Citation

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Barna,

Mátyás

2023

Preprint

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“…Regular diffusion is the cornerstone of many scientific disciplines, such as surface growth [6][7][8], reactions diffusion [9] or even flow problems in porous media. In our last two papers, we gave an exhaustive summary of such processes with numerous relevant reviews [10,11].…”

Section: Introductionmentioning

confidence: 99%

Even and Odd Self-Similar Solutions of the Diffusion Equation for Infinite Horizon

Mátyás

Barna

2023

Universe

Self Cite

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In the description of transport phenomena, diffusion represents an important aspect. In certain cases, the diffusion may appear together with convection. In this paper, we study the diffusion equation with the self-similar Ansatz. With an appropriate change of variables, we have found an original new type of solution of the diffusion equation for infinite horizon. We derive novel even solutions of diffusion equation for the boundary conditions presented. For completeness, the odd solutions are also mentioned as well, as part of the previous works. We have found a countable set of even and odd solutions, of which linear combinations also fulfill the diffusion equation. Finally, the diffusion equation with a constant source term is discussed, which also has even and odd solutions.

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“…Recent studies have used diferential equations to describe a variety of applications, such as [1][2][3][4][5][6][7][8]. Population models, a central topic in many sciences due to their signifcance, study population change over time.…”

Section: Introductionmentioning

confidence: 99%

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

Alebraheem

2023

Journal of Mathematics

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Predator interference refers to the competition effect on individuals of the same species through preventing or limiting access to a resource. In this paper, a novel predator–prey model that includes predator interference is considered. In the novel model, a high prey density is taken into consideration by investigating Crowley–Martin as a numerical response, while the growth rate of prey is logistically described and Holling type II is used as a functional response. In contrast to literature, this model has distinct and notable features: predator and prey species have an intraspecific competition, and this model has a numerical response that generalizes several of the commonly utilized depictions of predator interference. The boundedness of the model is proved. Predator interference effects are theoretically and numerically studied in terms of stability, coexistence, and extinction. Theoretical results show that the system has no effect on coexistence or extinction in these types of models. Numerical simulations present two different dynamics with identical results on the theoretical side of model stabilization for both dynamics. Moreover, the numerical simulations show that there is a change from periodic to steady state dynamics as the value of predator interference increases. This means that the coexistence probability of the model increases. The attained results are explained from both a mathematical and an ecological points of view.

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Advanced Analytic Self-Similar Solutions of Regular and Irregular Diffusion Equations

Cited by 9 publications

References 85 publications

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Analytic Solutions of the Complex Diffusion Equation with Possible Quantum Mechanical Relevance

Even and Odd Self-Similar Solutions of the Diffusion Equation for Infinite Horizon

Predator Interference in a Predator–Prey Model with Mixed Functional and Numerical Responses

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