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Counterexamples for parabolic differential equations. (English) Zbl 0331.35033


MSC:

35K10 Second-order parabolic equations
35K20 Initial-boundary value problems for second-order parabolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35K55 Nonlinear parabolic equations
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References:

[1] Hartman, P.: Ordinary differential equations. New York: John Wiley & Sons 1964 · Zbl 0125.32102
[2] Mlak, W.: An example of the equationu t =u xx +f(x, t, u) with distinct maximum and minimum solutions of a mixed problem. Ann. Polon. math.13, 101-103 (1963) · Zbl 0156.33502
[3] Protter, M. H., Weinberger, H. F.: Maximum principles in differential equations. New York: Prentice Hall 1967 · Zbl 0153.13602
[4] Szarki, J.: Differential inequalities. Monografic Matematycne, Vol. 43, Warszawa 1965
[5] Walter, W.: Differential and integral inequalities. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0252.35005
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