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Line method approximations to the Cauchy problem for nonlinear parabolic differential equations. (English) Zbl 0303.35046

MSC:
35K55Nonlinear parabolic equations
35A35Theoretical approximation to solutions of PDE
35B45A priori estimates for solutions of PDE
References:
[1]Friedman, A.: Partial differential equations of parabolic type. Prentice-Hall, Inc. Englewood Cliffs, N. J. (1964)
[2]Kamke, E.: Differentialgleichungen II, 4. Auflage. Leipzig: Akademische Verlagsgesellschaft 1962
[3]Kamynin, L. I.: On the convergence of a finite-difference process for the heat equation. (Russian.) Dokl. Akad. Nauk SSSR85, 701-714 (1952)
[4]Kamynin, L. I.: On the applicability of a finite-difference method to the solution of the heat equation, II. (Russian.) Izv. Akad. Nauk SSSR Ser. Mat.17, 249-268 (1953)
[5]Krzyza?skii, M.: Sur les solutions de léquation linéaire du type parabolique déterminées par les conditions initiales. Ann. Soc. Polon. Math.18, 145-156 (1945)
[6]Mlak, W., Olecb, C.: Integration of infinite systems of differential inequalities. Ann. Pol. Math. XIII, 105-112 (1963)
[7]Tychonoff, A.: Über unendliche Systeme von Differentialgleichungen. Mat. Sbornik41, 551-555 (1934)
[8]Voigt, A.: Die Linienmethode für das Cauchyproblem bei nichtlinearen parabolischen Differentialgleichungen. Dissertation. Universität karlsruhe (TH) (1971)
[9]Walter, W.: Die Linienmethode bei nichtlinearen parabolischen Differentialgleichungen. Num. Math.12, 307-321 (1968) · Zbl 0191.16902 · doi:10.1007/BF02162511
[10]Walter, W.: Gewöhnliche Differential-Ungleichungen im Banachraum. Arch. Math.20, 36-47 (1969a) · Zbl 0195.38402 · doi:10.1007/BF01898989
[11]Walter, W.: Approximation für das Cauchyproblem bei parabolischen Differentialgleichungen mit der Linienmethode. ISNM vol. 10, Abstract spaces and approximation, p. 139-145. Basel: Birkhäuser 1969b
[12]Walter, W.: Differential- und Integral-Ungleichungen. Springer tracts in natural philosophy, vol. 2. Berlin-Göttingen-Heidelberg-New York: Springer 1964
[13]Walter, W.: Differential and integral inequalities. Berlin-Heidelberg-New York: Springer 1970