School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road, Mumbai 400005, India
email: ktj@math.tifr.res.in
Kayyunnapara Thomas Joseph
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.
Submitted August 14, 2007. Published November 21, 2007.
Math Subject Classifications: 35B40, 35L65.
Key Words: Parabolic equations; exact solutions; asymptotic behaviour.
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Kayyunnapara Thomas Joseph School of Mathematics Tata Institute of Fundamental Research Homi Bhabha Road, Mumbai 400005, India email: ktj@math.tifr.res.in |
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