波動セミナー Asymptotic behavior toward a multi-wave pattern for the scalar viscous conservation law

開催日時
2014年   5月 23日 15時 00分 ~ 2014年   5月 23日 16時 30分
場所
北海道大学理学部3号館3-210室
講演者
松村 昭孝氏 (大阪大学大学院情報科学研究科)
 
In this talk, we show our recent works with
Natusmi Yoshida on the asymptotic behavior of solutions
to the Cauchy problems for the scalar viscous conservation law,
where the far field states are prescribed.
In particular, we treat the cases where the flux
function is convex but linearly degenerate on some
interval, and the corresponding Riemann solution
consists of a contact discontinuity and rarefaction waves.
As for the viscosity term, we treat the cases with
either a standard linear viscosity or a nonlinearly degenerate
viscosity term (p-Laplacian type viscosity (p>1)).
Then, for the standard linear viscosity (resp. the nonlinearly degenerate viscosity),
the solution of the viscous conservation law
is shown to asymptotically tend toward a multi-wave pattern
consisting of the rarefaction waves and a corresponding
viscous contact wave which is constructed by an integration of
the linear heat kernel (resp. the Barenblatt solution of the porous medium equation).


関連項目

研究集会・セミナー・集中講義の一覧へ