# Higher Order Asymptotics of Decaying Solutions of some Generalized Burgers Equations

@inproceedings{Braga2022HigherOA, title={Higher Order Asymptotics of Decaying Solutions of some Generalized Burgers Equations}, author={Gast{\~a}o A. Braga and Frederico Furtado and Jussara M. Moreira and Antonio Marcos da Silva}, year={2022} }

We study the large-time behavior of solutions to a generalized Burgers Equation, with initial zero mass data. Our main purpose is to present a modiﬁed version of the Renormalization Group map, which is able to provide the higher order asymptotic properties of the solution to the Cauchy problem of a class of nonlinear time-evolution problems.

## References

SHOWING 1-10 OF 12 REFERENCES

### Higher-order asymptotics of decaying solutions of some nonlinear, dispersive, dissipative wave equations

- Mathematics
- 1995

Considered herein are the generalized Korteweg-de Vries equations with a homogeneous dissipative term appended. Solutions of these equations that start with finite energy decay to zero as time tends…

### On the asymptotic behavior of solutions to nonlinear, dispersive, dissipative wave equations

- Mathematics
- 1994

### Numerical Renormalization Group Algorithms for Self-Similar Asymptotics of Partial Differential Equations

- MathematicsMultiscale Model. Simul.
- 2020

A numerical procedure is systematically studied that reveals the asymptotically self-similar dynamics of solutions of partial differential equations (PDEs) using the renormalizati approach.

### Renormalization Group and Asymptotics of Solutions of Nonlinear Parabolic Equations

- Mathematics
- 1993

We present a general method for studying long-time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It…

### DECAY OF SOLUTIONS TO NONLINEAR PARABOLIC EQUATIONS: RENORMALIZATION AND RIGOROUS RESULTS

- Physics, Mathematics
- 2003

Scaling and renormalization group (RG) methods are used to study
parabolic equations with a small nonlinear term and find the decay
exponents. The determination of decay exponents is viewed as an …

### Renormalization and scaling methods for nonlinear parabolic systems

- Mathematics
- 1997

We consider systems of nonlinear parabolic differential equations of the form where is a small positive number and is dimensionally consistent without additional dimensional constants. A systematic…

### Numerical simulation of universal finite time behavior for parabolic IVP via geometric renormalization group

- Mathematics
- 2017

A numerical procedure based on the renormalization group (RG) is presented. This procedure will compute the spatial profile and blow up time for self-similar behavior. This will be generated by a…

### Asymptotics of Partial Differential Equations and the Renormalisation Group

- Mathematics
- 1991

It is well-known that the asymptotics of partial differential equations (PDEs) may often be found from consideration of similarity solutions. In the examples usually encountered, the combinations of…

### Linear and nonlinear waves

- PhysicsScholarpedia
- 2009

The study of waves can be traced back to antiquity where philosophers, such as Pythagoras, studied the relation of pitch and length of string in musical instruments and the subject of classical acoustics was laid down and presented as a coherent whole by John William Strutt in his treatise Theory of Sound.