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By M. L. Ge, C. N. Yang

ISBN-10: 9971508281

ISBN-13: 9789971508289

ISBN-10: 9971508338

ISBN-13: 9789971508333

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43) the inequality L(z) ≤ 0 for |η | > N. 31), we have shown that L(z) ≤ 0 for all η , |η | = N. 45) where the constant N1 is chosen presently. 33) u1 D(s)ds ≥ 0 because U(0,t) ≤ u1 . We that z(0,t) ≥ 0; moreover, y(0,t) = U(0,t) also have φ (x, 0) = N1 z(x, 0) − y(x, 0), where z(x, 0) > 0. We may now choose N1 sufficiently large that both φ (0,t) and φ (x, 0) are greater than or equal to zero. 46) in view of the fact that L(y) = 0 and L(z) ≤ 0 for all η . ) ensures that φ ≥ 0 everywhere in E + , implying that y(x,t) ≤ N1 z(x,t) in E + .

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L. (1994) On the solution of the equation ut + un ux + H(x,t, u) = 0, Quart. Appl. Math. 52, 519–527. Lax, P. D. (1957) Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math. 10, 537–566. Mickens, R. E. (1988) Exact solutions to a population model: The logistic equation with advection, SIAM Rev. 30, 629–633. Murray, J. D. (1970a) Perturbation effects on the decay of discontinuous solutions of nonlinear first order wave equations, SIAM J. Appl. Math. 19, 273–298. Murray, J. D. (1970b) On the Gunn effect and other physical examples of perturbed conservation equations, J.

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Braid group, knot theory and statistical mechanics by M. L. Ge, C. N. Yang


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