Abstract
We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.
Original language | English (US) |
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Pages (from-to) | 683-695 |
Number of pages | 13 |
Journal | Transactions of the American Mathematical Society |
Volume | 311 |
Issue number | 2 |
DOIs | |
State | Published - 1989 |
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ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
Cite this
Stability of viscous scalar shock fronts in several dimensions. / Goodman, Jonathan.
In: Transactions of the American Mathematical Society, Vol. 311, No. 2, 1989, p. 683-695.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Stability of viscous scalar shock fronts in several dimensions
AU - Goodman, Jonathan
PY - 1989
Y1 - 1989
N2 - We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.
AB - We prove nonlinear stability of planar shock front solutions for viscous scalar conservation laws in two or more space dimensions. The proof uses the "integrated equation" and an effective equation for the motion of the front itself. We derive energy estimates that balance terms from the integrated equation with terms from the front motion equation.
UR - http://www.scopus.com/inward/record.url?scp=33646885643&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33646885643&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1989-0978372-9
DO - 10.1090/S0002-9947-1989-0978372-9
M3 - Article
AN - SCOPUS:33646885643
VL - 311
SP - 683
EP - 695
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 2
ER -