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A quasilinear parabolic and a related third order problem. (English) Zbl 0261.35049

35K55Nonlinear parabolic equations
35B45A priori estimates for solutions of PDE
Full Text: DOI
[1] Brezis, H.: Équations et inéquations non linéaires dans LES espaces vectoriels en dualité. Ann. inst. Fourier, Grenoble 18, 115-175 (1968)
[2] Browder, F. E.: Strongly nonlinear parabolic boundary value problems. Amer. J. Math. 86, 339-357 (1964) · Zbl 0143.33501
[3] Coleman, B. D.; Duffin, R. J.; Mizel, V. J.: Instability, uniqueness, and nonexistence theorems for the equation ut = uxx - uxtx on a strip. Arch. rational mech. Anal. 19, 100-116 (1965) · Zbl 0292.35016
[4] Coleman, B. D.; Noll, W.: Approximation theorem for functionals with applications in continuum mechanics. Arch. rational mech. Anal. 6, 355-370 (1960) · Zbl 0097.16403
[5] Hopf, E.: Über die anfangswertaufgabe für die hydrodynamischen grundgleichungen. Math. nach. 4, 213-231 (1950) · Zbl 0042.10604
[6] Ladyzenskaja, O. A.; Ural’ceva, N. N.: Boundary problems for linear and quasilinear parabolic equations. Amer. math. Soc. trans. Ser. 2 47, 217-299 (1956)
[7] Showalter, R. E.; Ting, T. W.: Pseudoparabolic partial differential equations. SIAM J. Math. anal. 1, 1-26 (1970) · Zbl 0199.42102
[8] Ting, T. W.: Certain non-steady flows of second order fluids. Arch. rational mech. Anal. 14, 1-26 (1963) · Zbl 0139.20105