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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

MSC:
35G15Boundary value problems for linear higher-order PDE
35B35Stability of solutions of PDE
35B45A priori estimates for solutions of PDE
References:
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[2]Markovitz, H., & B. D. Coleman, Adv. Appl. Mechanics 8, 69–101 (1964). · Zbl 0136.45104 · doi:10.1016/S0065-2156(08)70353-3
[3]Ting, T. W., Arch. Rational Mech. Anal. 14, 1–26 (1963). · Zbl 0139.20105 · doi:10.1007/BF00250690
[4]Markovitz, H., & B. D. Coleman, Phys. Fluids 7, 833–841 (1964). · Zbl 0151.40101 · doi:10.1063/1.1711294
[5]Truesdell, C., Phys. Fluids 7, 1134–1142 (1964). · doi:10.1063/1.1711352
[6]Stokes, G. G., Mathematical and Physical Papers, Vol. III. Cambridge: Cambridge University Press 1901.
[7]Lamb, H., Hydrodynamics. Cambridge: Cambridge University Press 1895.
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[9]Markovitz, H., & D. R. Brown, Trans. Soc. Rheology 7, 137–154 (1963). · doi:10.1122/1.548950
[10]Markovitz, H., Proc. Fourth Intern. Cong. Rheology (1963), in press.
[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.
[12]Hopf, E., Math. Nachrichten 4, 213–231 (1951).
[13]Coleman, B. D., Arch. Rational Mech. Anal. 9, 273–300 (1962).
[14]Courant, R., & D. Hilbert, Methods of Mathematical Physics, 1st English edition, Vol. 1. New York: Interscience 1953.
[15]Truesdell, C., U. S.Naval Res. Lab. Rep. No. P-3553 (1949) J. Math. pures appl. (9) 30, 111–158 (1951).
[16]Truesdell, C., J. Rational Mech. Anal. 1, 125–300 (1952).