Traveling-wave solutions of convection–di"usion systems by center manifold reduction
نویسنده
چکیده
A convection–di$usion system in one space dimension is a partial di"erential equation of the form ut + A(u)ux =(B(u)ux)x: (1.1) Here u∈Rn, and A(u) and B(u) are n×n matrices that we shall assume are C2 functions of u. If we ignore di"usion, we have the convection system ut + A(u)ux =0: (1.2) If A(u)=Df(u) for some 4ux function f : Rn → Rn, then Eq. (1.2) becomes ut + f(u)x =0; (1.3) a system of conservation laws, while Eq. (1.1) becomes ut + f(u)x =(B(u)ux)x; (1.4) a system of viscous conservation laws. The conservation law case occurs more often in applications and is far better studied; see [5] and [12]. However, equations of the
منابع مشابه
Traveling-wave Solutions of Convection-diffusion Systems by Center Manifold Reduction
Traveling waves u(x st) for systems of conservation laws ut + Df(u)ux = (B(u)ux)x were studied by Majda and Pego (J. Di erential Eqs. 56 (1985), 229{262) under the assumption that u( 1) and u(+1) are close. Their results were recently extended to general convection-di usion systems ut +A(u)ux = (B(u)ux)x by Sainsaulieu (SIAM J. Math. Anal. 27 (1996), 1286{1310). Sainsaulieu's proofs use xed-poi...
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