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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**Example text**

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. [14] M. Bertsch and R. Dal Passo, Hyperbolic Phenomena in a Strongly Degenerate Parabolic Equation, Arch Rational Mech. Anal. 117 (1992), 349–387. [15] Ph. Blanc, On the regularity of the solutions of some degenerate parabolic equations, Comm. in Partial Diﬀ. Equat. 18 (1993), 821–846. [16] 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.