By Amann H. (Ed)
Günter Lumer was once a very good mathematician whose paintings has nice effect at the study group in mathematical research and evolution equations. He used to be on the starting place of the breath-taking improvement the idea of semigroups observed after the pioneering ebook of Hille and Phillips of 1957. This quantity includes invited contributions providing the state-of-the-art of those issues and reflecting the large pursuits of Günter Lumer.
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Additional info for Functional Analysis and Evolution Equations: The Gunter Lumer Volume
4) Moreover, it is easy to see that for each R > 0, there is a constant M = M (R) > 0, such that a(z, ξ) ≤ M ∀ (z, ξ) ∈ R × RN , |z| ≤ R. 5) We also assume that a(z, 0) = 0 for all z ∈ R, and a(z, ξ) = zb(z, ξ) with b(z, ξ) ≤ M0 We consider the function h : R × R ∀ (z, ξ) ∈ R × RN , |z| ≤ R. 6) → R deﬁned by h(z, ξ) := a(z, ξ) · ξ. 7) h(z, ξ) ≥ 0 ∀ ξ ∈ RN , z ∈ R. 8) N for some positive continuous function M (z) and for any (z, ξ) ∈ R × R . 9) for any (z, ξ) ∈ R × R where D1 (z) = D0 (z) + f (z, 0).
Pazy, Evolution Equations Governed by Accretive Operators. Book in preparation.  M. Bertsch and R. Dal Passo, Hyperbolic Phenomena in a Strongly Degenerate Parabolic Equation, Arch Rational Mech. Anal. 117 (1992), 349–387.  Ph. Blanc, On the regularity of the solutions of some degenerate parabolic equations, Comm. in Partial Diﬀ. Equat. 18 (1993), 821–846.  Y. Brenier, Derivation of the Euler equations from a caricature of Coulomb interaction, Comm. Math. Physics 212 (2000), 93–104.
M. Maz´ on distributional terms. 4) where the initial condition u0 is assumed to be positive. In this case u represents u5/2 ux the temperature of electrons and the form of the conductivity a(u, ux ) = 1+u|u x| has the eﬀect of limiting heat ﬂux. Thus, existence and uniqueness results for higher-dimensional problems were not considered. 5) for some positive constants C0 , D0 , M0 . 6) for any (z, ξ) ∈ R × RN , and some positive and continuous functions C0 , D0 , M0 , such that C0 (z) > 0 for any z = 0.