On the Existence and Uniqueness of Solutions of the Equation
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 181-187

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The existence and uniqueness of strong global solutions of initial-boundary value problems for the quasilinear equation utt—∂σi(uxi)/∂xi—ΔNut= f is established for functions σi(ξ), i = 1, ..., N, satisfying: σi,(ξ) ∊ C1(-∞, ∞), σi(0) = 0 and for some constant K0.
On the Existence and Uniqueness of Solutions of the Equation. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 181-187. doi: 10.4153/CMB-1975-036-1
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[1] 1. Ladyzenskaja, O. A., Solonnikov, V. A. and Uralceva, N. N., Linear andquasilinear equations of parabolic type, A.M.S. Trans, of Math. Monographs, Vol. 23. Google Scholar

[2] 2. Ladyzenskaja, O. A. and Vralcera, N. N., Linear andquasilinear elliptic equations, Math, in Sc. and Eng. Vo., 46 (1968). Google Scholar

[3] 3. Lions, J. L., Quelques methods de résolution des problémes aux limits non linéaires, Dunod, Gauthier-Villars, Paris 1969. Google Scholar

[4] 4. Lions, J. L. and Strauss, W. A., Some nonlinear evolution equations, Bull. Soc. Math. France 93 (1965), 43-96. Google Scholar

[5] 5. MacCamy, R. C. and Mizel, V. J., Existence and non-existence in the large of solutions to quasilinear wave equations, Arch. Rational Mech. Anal., 25 (1967) 299-320. Google Scholar

[6] 6. MacCamy, R. C., Mizel, V. J. and Greenberg, J. M., On the existence, uniqueness and stability of solutions of the equation σ'(u)u+λu=pu: Jour. Math, and Mech., 17 (1968), 707-728. Google Scholar

[7] 7. Sather, Jerome, The existence of a global classical solution of the initial-boundary value problem for ☐u+u3=f, Arch. Rational Mech. Anal. 22 (1966), 292-307. Google Scholar

[8] 8. Stoker, J. J., Topics in nonlinear elasticity, Courant Inst, of Math. Se, N.Y. Univ., 1964. Google Scholar

[9] 9. Tsutsumi, M., Some nonlinear evolution equations of second order, Proc. Japan Acad., 47 (1971), 950-955. Google Scholar

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