TY - JOUR

T1 - Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation

AU - Schochet, Steven

N1 - Funding Information:
by NSF Postdoctoral Fellowship DMS84-14107. Current address: School of Sciences, Tel-Aviv University, Ramat Aviv 69978, Israel.

PY - 1987/7

Y1 - 1987/7

N2 - A short-time existence theorem is proven for the initial-boundary-value problem for a class of quasilinear symmetric hyperbolic systems containing a constant-coefficient spatial operator multiplied by a large parameter λ. Solutions u are shown to remain bounded independently of λ for a time independent of λ provided that u(0) and ul(0) are bounded independently of λ and certain structural conditions are satisfied. This result is applied to the quasigeostrophic approximation of the shallow water equations and the constant-pressure approximation in combustion, and solutions for these cases are shown to converge to solutions of limiting equations as λ → ∞.

AB - A short-time existence theorem is proven for the initial-boundary-value problem for a class of quasilinear symmetric hyperbolic systems containing a constant-coefficient spatial operator multiplied by a large parameter λ. Solutions u are shown to remain bounded independently of λ for a time independent of λ provided that u(0) and ul(0) are bounded independently of λ and certain structural conditions are satisfied. This result is applied to the quasigeostrophic approximation of the shallow water equations and the constant-pressure approximation in combustion, and solutions for these cases are shown to converge to solutions of limiting equations as λ → ∞.

UR - http://www.scopus.com/inward/record.url?scp=38249033919&partnerID=8YFLogxK

U2 - 10.1016/0022-0396(87)90178-1

DO - 10.1016/0022-0396(87)90178-1

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AN - SCOPUS:38249033919

VL - 68

SP - 400

EP - 428

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 3

ER -