Stability and Asymptotic Behavior of Periodic Traveling Wave Solutions of Viscous Conservation Laws in Several Dimensions |
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Authors: | Myunghyun Oh Kevin Zumbrun |
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Institution: | 1. Department of Mathematics, University of Kansas, Kansas, USA 2. Department of Mathematics, Indiana University, Indianapolis, USA
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Abstract: | Under natural spectral stability assumptions motivated by previous investigations of the associated spectral stability problem,
we determine sharp L
p
estimates on the linearized solution operator about a multidimensional planar periodic wave of a system of conservation laws
with viscosity, yielding linearized L
1 ∩ L
p
→ L
p
stability for all
p \geqq 2{p \geqq 2} and dimensions
d \geqq 1{d \geqq 1} and nonlinear L
1 ∩ H
s
→ L
p
∩ H
s
stability and L
2-asymptotic behavior for
p\geqq 2{p\geqq 2} and
d\geqq 3{d\geqq 3} . The behavior can in general be rather complicated, involving both convective (that is, wave-like) and diffusive effects. |
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Keywords: | |
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