TY - JOUR
T1 - Generic regularity of conservative solutions to a nonlinear wave equation
AU - Bressan, Alberto
AU - Chen, Geng
N1 - Publisher Copyright:
© 2015 Elsevier Masson SAS
PY - 2017
Y1 - 2017
N2 - The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u)(c(u)ux)x = 0. For an open dense set of C3 initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.
AB - The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u)(c(u)ux)x = 0. For an open dense set of C3 initial data, we prove that the solution is piecewise smooth in the t–x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a semilinear system with smooth coefficients, followed by an application of Thom's transversality theorem.
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U2 - 10.1016/j.anihpc.2015.12.004
DO - 10.1016/j.anihpc.2015.12.004
M3 - Article
AN - SCOPUS:85006635375
SN - 0294-1449
VL - 34
SP - 335
EP - 354
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 2
ER -