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A coupled non-linear hyperbolic-Sobolev system. (English) Zbl 0361.35045


MSC:

35L60 First-order nonlinear hyperbolic equations
35K55 Nonlinear parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:

[1] Agmon, S., Lectures on Elliptic Boundary Value Problems (1965), New York: Van Nostrand, New York · Zbl 0151.20203
[2] Barenblatt, G. I.; Zheltov, I. P.; Kochina, I. N., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., 24, 1286-1303 (1960) · Zbl 0104.21702
[3] J. R. Cannon - R. E. Ewing,A coupled non-linear hyperbolic-parabolic system, J. Math. Anal. and Appl. (to appear). · Zbl 0355.35063
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[5] Courant, R.; Hilbert, D., Methods of Mathematical Physics, 2 vols. (1962), New York: Wiley and Sons, New York · Zbl 0729.35001
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[8] Hurewicz, W., Lectures on Ordinary Differential Equations (1958), Cambridge, Mass.: The M.I.T. Press, Cambridge, Mass. · Zbl 0082.29702
[9] Petrovskii, I. G., Partial Differential Equations (1967), Philadelphia, Pennsylvania: W. B. Saunders Company, Philadelphia, Pennsylvania
[10] Showalter, R. E., Existence and representation theorems for a semilinear Sobolev equation in a Banach space, SIAM J. Math. Anal., 3, 527-543 (1972) · Zbl 0262.34047
[11] Showalter, R. E., Weak solutions of non-linear evolution equations of Sobolev-Galpern type, J. of Diff. Eqns., 11, 252-265 (1972) · Zbl 0232.35027
[12] Showalter, R. E.; Ting, T. W., Pseudo-parabolic partial differential equations, SIAM J. Math. Anal., 1, 1-26 (1970) · Zbl 0199.42102
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