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In this article, we investigate an initial-boundary value problem posed for generalized Burgers equation (GBE) with linear damping via the method of matched asymptotic expansions. Asymptotic solutions are constructed for different sub-regions of the domain |$x > 0,~ t > 0$|⁠. A special solution is derived, and it describes the large-time asymptotic behavior of the solutions of the GBE for certain parametric ranges. We also observe that a stationary solution of the GBE describes the large-time behavior of solutions for certain parametric ranges. The existence and uniqueness of the relevant stationary solution are proved using a shooting argument. A numerical study is presented comparing the numerical solutions (obtained by the method of lines) with the asymptotic solutions constructed. [ABSTRACT FROM AUTHOR]

This paper concerns the separable solutions of a generalized Burgers equation. Existence of separable solutions to the generalized Burgers equation is proved under certain conditions. A careful numerical study shows that these separable solutions of the generalized Burgers equation describe the large time asymptotic behavior of solutions of initial boundary value problems. [ABSTRACT FROM AUTHOR]

In this article, we construct solutions of a nonhomogeneous Burgers equation subject to certain unbounded initial profiles. In an interesting study, Kloosterziel [ 1 ] represented the solution of an initial value problem (IVP) for the heat equation, with initial data in , as a series of the self-similar solutions of the heat equation. This approach quickly revealed the large time behavior for the solution of the IVP. Inspired by Kloosterziel [ 1 ]'s approach, we express the solution of the nonhomogeneous Burgers equation in terms of the self-similar solutions of a linear partial differential equation with variable coefficients. Finally, we also obtain the large time behavior of the solution of the nonhomogeneous Burgers equation. [ABSTRACT FROM AUTHOR]

In this paper, we construct asymptotic N-wave solutions for the nonplanar Burgers equation as via a balancing argument. These constructed asymptotics are compared with the approximate solutions of the nonplanar Burgers equation obtained by an approach due to Parker ( Acoust. Lett. 4 (1981)). We also present a computationally convenient form for the N-wave solution of the nonplanar Burgers equation modifying Sachdev et al.'s ( Stud. Appl. Math. 103 (1999)) approach. The asymptotic N-wave solutions obtained by balancing argument and modification to Sachdev et al.'s approach are validated by a careful numerical study. [ABSTRACT FROM AUTHOR]

In this paper, we construct large-time asymptotic solution of the modified Burgers equation with sinusoidal initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study. [ABSTRACT FROM AUTHOR]

In this article, evolution of N-waves under the nonplanar Burgers equation, which takes into account geometrical expansion or contraction, is treated analytically. An exact asymptotic solution, generalizing that for the planar Burgers equation, is given for the case of expansion. An approximate treatement, using a balancing argument, gives asymptotic analytic results for both expansion and contraction. The analysis is fortified by an accurate numerical solution of the problem. This study is brought in close conjunction with the earlier work of Crighton and Scott [13] and Sachdev, Joseph and Nair [3]. [ABSTRACT FROM AUTHOR]