Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
نویسندگان
چکیده
We prove the existence of globally attracting solutions of viscous Burgers’ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomous forcing. The attracting solution is periodic if the forcing is periodic. The method is general and can be applied to other similar partial differential equations. The proof is computer assisted.
منابع مشابه
cient algorithms for rigorous integration forward in time of dPDEs . Existence of globally attracting xed points of viscous Burgers equation with constant forcing , a computer assisted proof
The dissertation is divided into two separate parts. First part We propose an e cient and generic algorithm for rigorous integration forward in time of systems of equations originating from partial di erential equations written in the Fourier basis. By rigorous integration we mean a procedure, which operates on sets, and return sets which are guaranteed to contain the exact solution. The algori...
متن کاملGlobal Dissipativity and Inertial Manifolds for Diffusive Burgers Equations with Low-Wavenumber Instability
Global well-posedness, existence of globally absorbing sets and existence of inertial manifolds is investigated for a class of diffusive Burgers equations. The class includes diffusive Burgers equation with nontrivial forcing, the Burgers-Sivashinsky equation and the QuasiStedy equation of cellular flames. The global dissipativity is proven in 2D for periodic boundary conditions. For the proof ...
متن کاملStationary Solutions for a Boundary Controlled Burgers' Equation
This paper is concerned with the stationary solutions of a one parameter family of boundary control problems for a forced viscous Burgers' equation. We assume that the forcing term possesses a special symmetry that greatly aids in our analysis. The parameter characterizing the family enters as a scalar gain in a proportional error boundary feedback control scheme. We show that as the gain varie...
متن کاملComparison of The LBM With the Modified Local Crank-Nicolson Method Solution of Transient Two-Dimensional Non-Linear Burgers Equation
Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...
متن کاملTraveling Waves of Some Symmetric Planar Flows of Non-Newtonian Fluids
We present some variants of Burgers-type equations for incompressible and isothermal planar flow of viscous non-Newtonian fluids based on the Cross, the Carreau and the power-law rheology models, and on a symmetry assumption on the flow. We numerically solve the associated traveling wave equations by using industrial data and in order to validate the models we prove existence and uniqueness of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Applied Dynamical Systems
دوره 14 شماره
صفحات -
تاریخ انتشار 2015