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Instability, uniqueness, and nonexistence theorems for the equation $u_t=u_{xx}-u_{xtx}$ on a strip. (English) Zbl 0292.35016

35G15Boundary value problems for linear higher-order PDE
35B35Stability of solutions of PDE
35B45A priori estimates for solutions of PDE
Full Text: DOI
[1] Coleman, B. D., & W. Noll, Arch. Rational Mech. Anal. 6, 355--370 (1960). · Zbl 0097.16403 · doi:10.1007/BF00276168
[2] Markovitz, H., & B. D. Coleman, Adv. Appl. Mechanics 8, 69--101 (1964). · Zbl 0136.45104 · doi:10.1016/S0065-2156(08)70353-3
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[5] Truesdell, C., Phys. Fluids 7, 1134--1142 (1964). · doi:10.1063/1.1711352
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[11] Serrin, J., in: Nonlinear Problems, Publication No. 8 of the Mathematics Research Center, U.S.Army, pp. 69--98. Madison: University of Wisconsin Press 1963.
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[14] Courant, R., & D. Hilbert, Methods of Mathematical Physics, 1st English edition, Vol. 1. New York: Interscience 1953. · Zbl 0051.28802
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[16] Truesdell, C., J. Rational Mech. Anal. 1, 125--300 (1952).