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References
1. Asrakulova D. and Elmurodov A.N., A reaction-diffusion-advection competition model with a free boundary, Uzbek Mathematical Journal №3, 25-37 (2021).
2. Bendahmane M., Analysis of a reaction-diffusion system modeling predatorprey with prey-taxis, Networks and Heterogeneous Media № 3, 863-879 (2008).
3. Cantrell R. S. and Cosner C., Spatial Ecology via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology, Wiley, Chichester, 760 (2003).
4. Dale P. D., Maini Ph. K. and Sheratt J. A., Mathematical Modeling of Corneal Epithelial Wound Healing, Mathematical Biosciences №24, 127-147 (1994).
5. Du Y. and Lin Z., Spreading–vanishing dichotomy in the diffusive logistic model with a free boundary, SIAM Journal on Mathematical Analysis, №42, 377–405 (2010).
6. Y. Du and Z. Lin, The diffusive competition model with free boundary: invasion of a superoir or inferior competitor,Disc.Contin.Dyn.Syst.Ser.B, №19 (10), 3105-3132 (2014).
7. Elmurodov A. N., The paper considers the two-phase Stefan problem for systems of reaction-diffusion equations, Uzbek Mathematical Journal №4, 54-64 (2019).
8. Elmurodov A. N., Two-phase problem with a free boundary for systems of parabolic equations with a nonlinear term of convection, Vestnik KRAUNC. Fiziko-Matematicheskie Nauki. №36, 3, 110-122 (2021).
9. Friedman A., Free boundary problems in biology, Discrete Contin. Dyn. Syst. №2, 9, 3081-3097 (2015).
10. Guo J. and Wu C., On a free boundary problem for a two-species weak competitor system, J. Dynam. Diff. Equations, № (4), 873--895 (2012).
11. Takhirov J. O. and Rasulov M. S., Problem with Free Boundary for Systems of Equations of Reaction-Diffusion Type, Ukrainian Math.J., №69 (12), 1968-1980 (2018).
12. Takhirov J. O. and Elmurodov A. N., On a mathematical model with a free boundary for water basin pollution, Uzbek Mathematical Journal №4, 44-57 (2020).
13. Takhirov J. O., On Relaxation Transport Models, Journal of Mathematical Sciences №254 (2), 305-317 (2021).
14. Takhirov J. O., Global existence of classical solutions to a chemotaxis-haptotaxis model, SN Partial Differential Equations and Applications № 2 (1), 1-15 (2021).
15 Takhirov J. O., A free boundary problem for a reaction-diffusion equation appearing in biology, Indian J. Pure Appl. Math., №50(1), 95-112 (2019).
16. Wang J. and Zhang L., Invasion by an inferior or superior competitor: A diffusive competitionmodel with a free boundary in a heterogeneous environment, J.
Math. Anal. Appl., №42(3), 377-398 (2015).
17. Wang M. X. and Zhang Y., Two kinds of free boundary problems for the diffusive prey-predator model, Nonlinear Anal.: Real World Appl., № 24, 73-82 (2015).
18. Wu C. H., The minimal habitat size for spreading in a weak competition system
with two free boundaries, J. Diff. Equat., №259, 873-897 (2015).
19. Ainseba B. E., Bendahmane M. and Noussair A., A reaction-diffusion system modeling predator-prey with prey-taxis, Nonlinear Analysis Real World Applications №9, 2086-2105 (2008).
20. Aziz-Alaoui M. A., and Daher-Okiye M. Boundedness and Global Stability or a Predator-prey Model with Modified Leslie-Gower and Holling-Type II Schemes,
Applied Mathematics Letters №16, 1069-1075 (2003).
21. Chen F., Chen L. and Xie X., On a Leslie-Gower predator-prey model incorporating a prey refuge,Nonlinear Analysis: Real World Applications №10, 2905-2908 (2009).
22. Chen X. and Friedman A., A free boundary problem arising in a model of wound healing, SIAM Journal on Mathematical Analysis №32, 788--800 (2000).
23. Leslie P. H., Gower J .C., The properties of a stochastic model for the predator-prey type of interaction between two species, Biometrika №47 (3-4), 219 (1960).
24. Lin Z. G., A free boundary problem for a predator-prey model, Nonlinearity №20, 1883-1892 (2007).
25. Liu Y., Guo Z., Smaily M. El, and Wang L., Biological invasion in a predator-prey model with a free boundary, Liu et al. Boundary Value Problems №2019:33, 22 (2019).
26. Peng R., and Wang M., Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model. Appl. Math.Lett. №20(6), 664-670 (2007).
27. Tanner J. T., The stability and the intrinsic growth rates of prey and predator populations, Ecology №56}, 855-867 (1975).
28. Tao Y., Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis, Nonlinear Analysis Real World Applications №11(3), 2056-2064 (2010).
29. Wang M., On some free boundary problems of the prey-predator model, J. Diff. Equations, №256(10), 3365-3394 (2014).
30. Wang M., Spreading and vanishing in the diffusive prey-predator model with a free boundary, Communications in Nonlinear Science and Numerical Simulation №23(1-3), 311--327 (2015).
31. Wang M., Zhao J., A free boundary problem for the predator-prey model with double free boundaries, J.Dynam.Diff.Equations, №29(3), 957--979(2017).
32. Zhang Y., Wang M., A free boundary problem of the ratio-dependent prey-predator model, Appl. Anal., №94(10), 2147--2167 (2015).
33. Kruzhkov S. N., Nonlinear parabolic equations with two independent variables, Trudy Moskov. Mat. Obs., Transl., №16, 329--346 (1967).
34. Ladyzhenskaja O. A., Solonnikov V. A., and Uralceva N. N., Linear and quasi-linear equations of parabolic type. Amer. Math. Soc. Transl., Providence, Rhode Island №23, 720 (1968).
35. Pao C. V., Nonlinear Parabolic and Elliptic Equations, New York, Plenum Press, 780 (1992).
36. Friedman A., Parabolic partial differential equations, Mir, 428 (1968).
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