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

35K55Nonlinear parabolic equations
35A35Theoretical approximation to solutions of PDE
35B45A priori estimates for solutions of PDE
Full Text: DOI EuDML
[1] Friedman, A.: Partial differential equations of parabolic type. Prentice-Hall, Inc. Englewood Cliffs, N. J. (1964) · Zbl 0144.34903
[2] Kamke, E.: Differentialgleichungen II, 4. Auflage. Leipzig: Akademische Verlagsgesellschaft 1962 · Zbl 0145.10003
[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) · Zbl 0051.07602
[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) · Zbl 0135.12704
[7] Tychonoff, A.: Über unendliche Systeme von Differentialgleichungen. Mat. Sbornik41, 551-555 (1934) · Zbl 0011.34902
[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 · Zbl 0252.35005