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Titlebook: Nonlinear Evolution Equations and Related Topics; Dedicated to Philipp Wolfgang Arendt,Haïm Brézis,Michel Pierre Book 2004 Springer Basel A

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Intrinsic metrics and Lipschitz functions,is respect, we bring some precisions and complements to [.], notably concerning links with the notion of intrinsic metric ([.]). In the particular case of an abstract Wiener space, we establish the relationship between these notions and that of .-metric ([.]) and µ-a.e. .-Lipschitz continuous function ([.]).
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On the regularizing effect of strongly increasing lower order terms,odel example is . where Ω is a bounded open set in ℝ., . is a continuous and increasing function such that ., for some δ>0.We also show a nonexistence result for some measures as data as in the model example . where . is the Dirac mass in ..(..∈Ω).
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Nonautonomous heat equations with generalized Wentzell boundary conditions,ptions, that there exists a unique evolution family for this problem and that the family satisfies various regularity properties. This enables us to obtain, for the corresponding inhomogeneous problem, classical and strict solutions having optimal regularity.
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Linearized stability for nonlinear evolution equations,ator A ⊂ .x . in a Banach space . that has a linear ‘resolvent-derivative’ Ã ⊂ . x .. The result is applied to derive linearized stability results for the case of A = . under ‘minimal’ differentiability assumptions on the operators . ⊂ . x . and . → at the equilibrium point, as well as for partial differential delay equations.
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