Mathematics / Matematik

Permanent URI for this collectionhttps://hdl.handle.net/11147/8

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Author: search.filters.author.Bozacı, Aylin

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  • Article
    Citation - WoS: 2
    Citation - Scopus: 6
    Dynamical Properties of Generalized Traveling Waves of Exactly Solvable Forced Burgers Equations With Variable Coefficients
    (Elsevier, 2021) Atılgan Büyükaşık, Şirin; Bozacı, Aylin
    The initial value problem for a generalized forced Burgers equation with variable coefficients U-t + ((mu)over dot(t)/mu(t))U + UUX = (1/2 mu(t))U-xx - a(t)U-x + b(t)(xU)(x) - omega(2)(t)x + f(t), x is an element of R , t > 0, is solved using Cole-Hopf linearization and Wei-Norman Lie algebraic approach for finding the evolution operator of the associated linear diffusion type equation. As a result, solution of the initial value problem is obtained in terms of a corresponding linear second-order inhomogeneous ordinary differential equation and a standard Burgers model. Then, using the translation and Galilean invariance of standard Burgers equation, families of generalized nonlinear waves propagating according to a Newtonian type equation of motion are constructed. The influence of the damping, dilatation and forcing terms on the dynamics of shocks, multi-shocks, triangular and N-shaped generalized traveling waves and rational type solutions with moving singularities is investigated. Finally, exactly solvable models with concrete time-variable coefficients are introduced and dynamical properties of certain particular solutions are discussed. (C) 2020 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 7
    Dirichlet Problem on the Half-Line for a Forced Burgers Equation With Time-Variable Coefficients and Exactly Solvable Models
    (Elsevier, 2020) Atılgan Büyükaşık, Şirin; Bozacı, Aylin
    We consider a forced Burgers equation with time-variable coefficients and solve the initial-boundary value problem on the half-line 0 < x < infinity with inhomogeneous Dirichlet boundary condition imposed at x = 0. Solution of this problem is obtained in terms of a corresponding second order ordinary differential equation and a second kind singular Volterra type integral equation. As an application of the general results, we introduce three different Burgers type models with specific damping, diffusion and forcing coefficients and construct classes of exactly solvable models. The Burgers problems with smooth time-dependent boundary data and an initial profile with pole type singularity have exact solutions with moving singularity. For each model we provide the solutions explicitly and describe the dynamical properties of the singularities depending on the time-variable coefficients and the given initial and boundary data. (C) 2019 Elsevier B.V. All rights reserved.