Asymptotic behaviour of soultions to nonlinear parabolic equations with variable viscocity and geometric terms

Joseph, Kayyunnapara Thomas (2007) Asymptotic behaviour of soultions to nonlinear parabolic equations with variable viscocity and geometric terms Electronic Journal of Differential Equations, 2007 (157). pp. 1-23. ISSN 1072-6691

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Abstract

In this paper we study the asymptotic behaviour of solutions of certain nonlinear parabolic equations with variable viscosity and geometric terms. We generalize the results on the large time behaviour and vanishing viscosity limits obtained earlier for planar Burgers equation by Hopf [7], Lighthill [20] and others. For several classes of systems of equations we derive explicit solution for initial value problem with different types of initial conditions and study large time behaviour of the solutions and its asymptotic form. We derive the simple hump solutions and N-wave solutions as its asymptotes depending on the conditions on the data and derive Lp decay estimates for solutions and show that they depend on the variable viscosity coefficient and geometric terms. We also analyse the small viscosity limit of these solutions.

Item Type:Article
Source:Copyright of this article belongs to The European Mathematical Information Service.
ID Code:83202
Deposited On:16 Feb 2012 12:15
Last Modified:19 May 2016 00:08

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