BCAM Seminar Hardy type inequality and application to the stability of degenerate stationary waves
Date: Fri, Sep 5 2008
Location: Kyushu University, Japan
Speakers: Shuichi KAWASHIMA
This paper is concerned with the asymptotic stability of degenerate
stationary waves for viscous conservation laws in the half space. It is
proved that the solution converges to the corresponding degenerate
stationary wave at the rate t−α/4 as t → ∞, provided that the initial
perturbation is in the weighted space L2
α = L2(R+; (1 + x)α) for α <
αc(q) := 3+2/q, where q is the degeneracy exponent. This restriction
on α is best possible in the sense that the corresponding linearized
operator can not be dissipative in L2
α for α > αc(q). Our stability
analysis is based on the space-time weighted energy method combined
with a Hardy type inequality with the best possible constant.
stationary waves for viscous conservation laws in the half space. It is
proved that the solution converges to the corresponding degenerate
stationary wave at the rate t−α/4 as t → ∞, provided that the initial
perturbation is in the weighted space L2
α = L2(R+; (1 + x)α) for α <
αc(q) := 3+2/q, where q is the degeneracy exponent. This restriction
on α is best possible in the sense that the corresponding linearized
operator can not be dissipative in L2
α for α > αc(q). Our stability
analysis is based on the space-time weighted energy method combined
with a Hardy type inequality with the best possible constant.
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