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Journal of Applied Mathematics and Computing

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04.08.2021 | Original Research

Regularity and solution profiles along propagation for a cooperative species system with non-linear diffusion

verfasst von: José Luis Díaz Palencia

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 4/2022

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Abstract

The present analysis provides insights and analytical findings for a cooperative system formulated with non-linear diffusion. This work discusses, from an analytical perspective, the interaction of two species when both cooperate to explore new territories. Firstly, the analysis focuses on regularity, existence and uniqueness of weak solutions considering slightly positivity in the non-linear operator together with a monotone argument in the independent terms. Afterwards, analytical solution profiles are provided making use of selfsimilar solutions. Non-linear diffusion induces the existence of a propagating front and determines the property of finite speed of propagation in both species when they cooperate to explore new territories.

Vorheriger Artikel A study on some operations and products of neutrosophic hypersoft graphs

Nächster Artikel Predator–prey system with multiple delays: prey’s countermeasures against juvenile predators in the predator–prey conflict

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Ahn, J., Yoon, C.: Global well-posedness and stability of constant equilibria in parabolic-elliptic chemotaxis system without gradient sensing. Nonlinearity 32, 1327–1351 (2019)MathSciNetCrossRef

Alford J.G.: Mathematical Models Can Predict the Spread of an Invasive species. In: Sriraman B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham.(2019)

Banani, R., Sankar, K.R., Biswas, M.H.A.: Effects on prey-predator with different functional responses. Int. J. Biomath. 10, 08 (2017)MathSciNetMATH

Bedrossian, J., Rodríguez, N., Bertozzi, A.: Local and global wellposedness for aggregation equations and patlak-keller-segel models with degenerate diffusion. Nonlinearity 24(6), 1683 (2001)CrossRef

Bertozzi, A., Slepcev, D.: Existence and uniqueness of solutions to an aggregation equation with degenerate diffusion. Commun. Pure Appl. Anal. 9(6), 1617 (2009)MathSciNetCrossRef

Bertsch, M., Hilhorst, D.: A density dependent diffusion equation in population dynamics: stabilization to equilibrium. SIAM J. Math. Anal. 17(4), 863–883 (1986)MathSciNetCrossRef

Bhatti, M., Zeeshan, A., Ellahi, R., Anwar Bég, O., Kadir, A.: Effects of coagulation on the two-phase peristaltic pumping of magnetized prandtl biofluid through an endoscopic annular geometry containing a porous medium. Chin. J. Phys. (2019). https://doi.org/10.1016/j.cjph.2019.02.004CrossRef

Boyadzhiev, G.: Existence theorems for cooperative systems of parabolic PDEs and applications in chemistry. AIP Conference Proceedings 2159(1), 030004 (2019). https://doi.org/10.1063/1.5127469CrossRef

Cho, E., Kim, Y.J.: Starvation driven diffusion as a survival strategy of biological organisms Bull. Math. Biol. 75, 845–870 (2013)MathSciNetCrossRef

10.

De Pablo, A.: Doctoral Thesis. Estudio de una ecuación de reacción - difusión Universidad Autónoma de Madrid (1989)

11.

De Pablo, A., Vázquez, J.L.: Travelling waves and finite propagation in a reaction-diffusion Equation. J. Differ Equ. 93, 19–61 (1991)MathSciNetCrossRef

12.

Díaz, J.: Modeling of an aircraft fire extinguishing process with a porous medium equation. SN Appl. Sci. (2020). https://doi.org/10.1007/s42452-020-03891-9CrossRef

13.

Díaz, J.L., Fernández, M.: Non-linear parabolic predator prey coupled system with convections. Int. J. Biomath. (2020). https://doi.org/10.1142/S1793524521500054CrossRef

14.

Ellahi, R., Hussain, F., Ishtiaq, F., et al.: Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: An application to upgrade industrial sieves/filters. Pramana J. Phys. 93, 34 (2019). https://doi.org/10.1007/s12043-019-1781-8CrossRef

15.

Foldes, J., Polacik, P.: On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry. Discrete Cont. Dynam. Syst. 25(1), 133–157 (2009). https://doi.org/10.3934/dcds.2009.25.133MathSciNetCrossRefMATH

16.

Haiyin, Li.: Hopf Bifurcation of delayed density-dependent Predator-Prey model. Acta Math. Sci. Series A. 39(2), 358–371 (2019)

17.

Jones, B.F.: Singular Integrals and Parabolic Equations. American Mathematical Society, United States of America (1963)CrossRef

18.

Karátson, J.: A maximum principle for some nonlinear cooperative elliptic PDE systems with mixed boundary conditions. J. Math. Anal. Appl. 44(2), 900–910 (2016). https://doi.org/10.1016/j.jmaa.2016.06.062MathSciNetCrossRefMATH

19.

Keller, E.F., Segel, L.A.: Traveling bands of chemotactic bacteria: a theoretical analysis. J. Theoret. Biol. 30, 235–248 (1971)CrossRef

20.

King-Yeung, L., Xueying, W., Tianran, Z.: Traveling waves for a class of diffusive disease transmission modells with network structures. SIAM J. Math Anal. 60(6), 5719–5748 (2018)MATH

21.

Rubenstein, D., Kealey, J.: Cooperation, Conflict, and the Evolution of Complex Animal Societies. Nat. Edu. Knowl. 3(10), 78 (2010)

22.

Pao, C.: Nonlinear Parabolic and Elliptic Equations. Springer Science+Bussiness Media. North Carolina, United States of America (2012)

23.

Piccoli, B., Rossi, F. and Trélat, E.: Sparse control of second-order cooperative systems and partial differential equations to approximate alignment * (2016)

24.

Shahid, A., Huang, H., Bhatti, M.M., Zhang, L., Ellahi, R.: Numerical investigation on the swimming of gyrotactic microorganisms in nanofluids through porous medium over a stretched surface. Mathematics 8, 380 (2020). https://doi.org/10.3390/math803038CrossRef

25.

Tao, Y., Winkler, M.: Effects of signal-dependent motilities in a keller-segel-type reactiondiffusion system. Math. Models Methods Appl. Sci. 27, 1645 (2017)MathSciNetCrossRef

26.

Vázquez, J.L.: The Porous Medium Equation. Mathematical Theory. Oxford Mathematical Monographs, Oxford (2006)CrossRef

27.

Yoon, C., Kim, Y.J.: Global existence and aggregation in a keller-segel model with fokker- Planck diffusion. Acta Appl. Math. 149, 101 (2016)MathSciNetCrossRef

28.

Zhang, Y.: Degenerate Diffusion with Advection. Doctoral Thesis. University of California (2019)

29.

Zu, L., Jiang, D., O’Regan, D.: Periodic solution for a stochastic non-autonomous Predator-Prey model with Holling II functional response. Acta Appl. Math. 161, 89–105 (2019) cta Appl. Math. 161, 89–105 (2019). https://doi.org/10.1007/s10440-018-0205-y

Titel: Regularity and solution profiles along propagation for a cooperative species system with non-linear diffusion
verfasst von: José Luis Díaz Palencia
Publikationsdatum: 04.08.2021
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 4/2022
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-021-01616-8

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