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A generalized maximum principle and estimates of max vrai u for nonlinear parabolic boundary value problems. (English) Zbl 0344.35049
MSC:
35K55 Nonlinear parabolic equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B45 A priori estimates in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:
[1] J. Kačur : Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order. (I, II).
[2] J. Kačur: Application of Rothe’s method to nonlinear evolution equations. Mat. Časopis Sloven. Akad. Vied, 25, (1975), N-1, 63-81.
[3] П. П. Мосолов: Вариационные методы в нестационарных задачах. (Параболический случай) Изв. АН СССР, 34 (\? 1970), 425-457. · Zbl 1170.92319
[4] K. Rektorys: On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables. Czech. Math. Journal, 21 (96) 1971, 318-339. · Zbl 0217.41601
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[8] J. Nečas: Les méthodes directes en théorie équations elliptiques. Prague, 1967. · Zbl 1225.35003
[9] A. Friedman: Partial differential equations of parabolic type. Prentice-Hall, INC, 1964. · Zbl 0144.34903
[10] О. А. Ладыженская В. А. Солонников Н. Н. Уральцева: Линейные и квазилинейные уравнения параболического типа. ,Hauka”, Москва 1967. · Zbl 1204.62024
[11] J. Kačur: On boundedness of the weak solution for some class of quasilinear partial differential equations. Časopis Pěst. Mat., 98 (1973), 43 - 55.
[12] М. А. Красносельский: Топологические методы в теории нелинейных интегральных уравнений. Москва, 1956. · Zbl 0995.90522
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