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Existence and nonexistence of global solutions for nonlinear parabolic equations. (English) Zbl 0248.35074

MSC:
35K55 Nonlinear parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
35K20 Initial-boundary value problems for second-order parabolic equations
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[1] Fujita, H., On some nonexistence and nonuniqueness theorems for nonlinear parabolic equations. Proc. Symp. in Pure Math. 18, American Mathematical Society, Providence, Rhode Island, (1970), 105-113. · Zbl 0228.35048
[2] Lions, J.-L., Quelques Methodes de Resolution des Problemes aux Limites non Lineaires, Dunod, Paris, 1969. · Zbl 0189.40603
[3] Ladyzhenskaya, O. A., V. A. Solonnikov and N. N. Uralceva, Linear and Quasilinear Parabolic Equations, ”Nauka”, Moscow, 1967; English transl., Trans. Math. Monographs, 23, American Mathematical Society, Providence, Rhode Island, 1968.
[4] Sattinger, D. H., On global solution of nonlinear hyperbolic equations, Arch. Rat. Mech. Anal 30 (1968), 148-172. · Zbl 0159.39102
[5] Friedman, A., Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, N. J., 1964. · Zbl 0144.34903
[6] Sobolevskii, P. E. Local and nonlocal existence theorems for nonlinear second- order parabolic equations, Dokl. Akad. Nauk SSSR, 136 (1961), 292-295. · Zbl 0196.40301
[7] Aubin, J.P., Un theoreme de compacite, C. R. Acad. Sci. Paris, 256 (1963), 5042-5044. · Zbl 0195.13002
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