On the evolution of solutions of Burgers equation on the positive quarter-plane

• Autorzy: Hanaç Esen

Identyfikatory

DOI

10.1515/dema-2019-0020

• Języki publikacji: EN

Abstrakty

EN

In this paper we investigate an initial-boundary value problem for the Burgers equation on the positive quarter-plane; vt + vvx - vxx = 0, x>0, t>0, v(x,0) = u+, x>0, v(0,t) = ub, t>0, where x and t represent distance and time, respectively, and u+ is an initial condition, ub is a boundary condition which are constants (u+ ≠ ub). Analytic solution of above problem is solved depending on parameters (u+ and ub) then compared with numerical solutions to show there is a good agreement with each solutions.

Słowa kluczowe

EN

Burgers equation; traveling wave; numerical solutions

PL

równanie Burgersa; fala bieżąca; rozwiązania numeryczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 237--248
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Hanaç Esen

• Department of Mathematics, Adıyaman University, Turkey

Bibliografia

• [1] Aronson D. G., Weinberger H. F., Multidimensional nonlinear diffusion arising in propagation genetics, Adv. Math., 1978, 30(1), 33–76
• [2] Aronson D. G., Weinberger H. F., Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, In: Goldstein J. A. (Ed.), Partial Differential Equations and Related Topics, Springer Berlin, Lecture Notes in Mathematics, 1975, 446, 5–49
• [3] Bramson M. D., Maximal displacement of branching Brownian motion, Comm. Pure Appl. Math., 1978, 31, 531–582
• [4] Burgers J. M., A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech., 1948, 1, 171–199
• [5] Burgers J. M., Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion, Kon. Ned. Akad. Wet., Verh. (Eerste Sectie), 1939, 17(2), 1–53
• [6] Hanaç E., The large-time solution of nonlinear evolution equations, Ph. D. Thesis, University of Birmingham, 2015
• [7] Leach J. A., Needham D. J., Matched asymptotic expansions in reaction-diffusion theory, Springer Monographs in Mathematics, Springer-Verlag London, 2004
• [8] Leach J. A., Hanaç E., On the evolution of travelling wave solutions of the Burgers-Fisher equation, Quart. Appl. Math., 2016, 74, 337–359
• [9] Hanaç E., The phase plane analysis of nonlinear equation, J. Math. Anal., 2018, 9, 89–97
• [10] Landejuela M., Burgers equation, BCAM Internship report: Basque Center for Applied Mathematics, 2011

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).