Large time asymptotics for solutions to a nonhomogeneous Burgers equation

Chidella, S. R.; Yadav, Manoj Kumar

doi:10.1007/s10483-010-1352-9

Cited by 7 publications

(6 citation statements)

References 10 publications

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“…Finally, we note that for the above particular solutions, one has lim t!1 Uðx; tÞ ¼xx. Similar result was obtained in [22], where the long-time asymptotics for solutions of the BE (30) were discussed according to the properties of the initial profile. …”

Section: Forced Burgers Equation With Time Dependent Coefficientssupporting

confidence: 80%

Exact solutions of forced Burgers equations with time variable coefficients

Büyükaşık¹,

Pashaev²

2013

Communications in Nonlinear Science and Numerical Simulation

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a b s t r a c tIn this paper, we consider a forced Burgers equation with time variable coefficients of the form2 ðtÞx, and obtain an explicit solution of the general initial value problem in terms of a corresponding second order linear ordinary differential equation. Special exact solutions such as generalized shock and multi-shock waves, triangular wave, N-wave and rational type solutions are found and discussed. Then, we introduce forced Burgers equations with constant damping and an exponentially decaying diffusion coefficient as exactly solvable models. Different type of exact solutions are obtained for the critical, over and under damping cases, and their behavior is illustrated explicitly. In particular, the existence of inelastic type of collisions is observed by constructing multi-shock wave solutions, and for the rational type solutions the motion of the pole singularities is described.

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Section: Forced Burgers Equation With Time Dependent Coefficientssupporting

confidence: 80%

Exact solutions of forced Burgers equations with time variable coefficients

Büyükaşık¹,

Pashaev²

2013

Communications in Nonlinear Science and Numerical Simulation

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“…where in (2) and (3) A and B are free parameters and v is the velocity of the wave. Also, the unknown exponent p will be determined during the course of the derivation of the soliton solution to (1).…”

Section: +1 Dimensionsmentioning

confidence: 99%

“…This equation has been exhaustively studied by various scientists all over the globe [1][2][3][4][5][6][7][8][9][10]. It appears in various areas of physical sciences.…”

Section: Introductionmentioning

confidence: 99%

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1-Soliton solution of the generalized Burgers equation with generalized evolution

Biswas

Triki

Hayat

et al. 2011

Applied Mathematics and Computation

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“…Ding and Ding showed that, for fixed

(x, t),

the solution of converges to the weak solution of relevant inviscid FBE as

μ \to 0 .

Chidella and Yadav constructed solutions to the FBE subject to the initial data containing bounded and compactly supported initial profiles. Rao and Yadav obtained the solutions to a generalization of , namely,

u_{t} + u u_{x} = u_{x x} + \frac{k x}{{false(2 β t + 1 false)}^{2}}, x \in R, t > 0 .

They reduced to the linear equation

φ_{t} = φ_{x x} - \frac{k x^{2}}{4 {(2 β t + 1)}^{2}} φ, x \in R, t > 0,

via Cole–Hopf transformation and then expressed the solution of in terms of self‐similar solutions of concerned heat equation.…”

Section: Introductionmentioning

confidence: 99%

Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation

2016

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This article deals with a forced Burgers equation (FBE) subject to the initial function, which is continuous and summable on double-struckR. Large time asymptotic behavior of solutions to the FBE is determined with precise error estimates. To achieve this, we construct solutions for the FBE with a different initial class of functions using the method of separation of variables and Cole–Hopf like transformation. These solutions are constructed in terms of Hermite polynomials with the help of similarity variables. The constructed solutions would help us to pick up an asymptotic approximation and to show that the magnitude of the difference function of the true and approximate solutions decays algebraically to 0 for large time.

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Large time asymptotics for solutions to a nonhomogeneous Burgers equation

Cited by 7 publications

References 10 publications

Exact solutions of forced Burgers equations with time variable coefficients

Exact solutions of forced Burgers equations with time variable coefficients

1-Soliton solution of the generalized Burgers equation with generalized evolution

Large Time Asymptotics with Error Estimates to Solutions of a Forced Burgers Equation

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