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Gutachter: Quasilinear parabolic pr
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Contents 1 Introduction 3 2 Prelimi
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Chapter 1 Introduction The present
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to assume that m, c are bounded fun
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We give now an overview of the cont
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conditions of order ≤ 1. Sections
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Chapter 2 Preliminaries 2.1 Some no
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Clearly, φA ∈ [0, π) and φA
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Definition 2.2.3 Let X and Y be Ban
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µ ∈ Σφα }. Let N ∈ N, Tj
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We remark that a theorem of the Dor
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Here f(A, ·) ∈ H0(Σ π 2 +η; B
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Further, K ∞ (α, θa) := {a ∈
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Using (2.19) for aω and bω yields
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2.7 Evolutionary integral equations
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Example 2.8.1 For J = [0, T ] and a
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We conclude this section by illustr
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kernel a. The operator B is inverti
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x := f(0) ∈ X exists and we are l
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with two positive constants C1, C2
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with two positive constants C1 and
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derivative theorem to this pair of
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3.2 A general trace theorem Let X b
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3.3 More time regularity for Volter
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Theorem 3.4.2 Suppose X is a Banach
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Our next objective is to show neces
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Let u1 be the restriction of v1 to
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Proof. We begin with the necessity
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Chapter 4 Linear Problems of Second
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The strategy for solving (4.1) is n
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Since ψj ≡ 1 on supp ϕj, we may
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Turning to (c), let g ∈ Ξi+1 and
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- Page 81 and 82: Chapter 5 Linear Viscoelasticity In
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- Page 87 and 88: To see the converse direction, supp
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- Page 97 and 98: Chapter 6 Nonlinear Problems 6.1 Qu
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- Page 101 and 102: (d) bD ∈ C(J0 × ΓD × U0), ∃C
- Page 103 and 104: which entails (6.14). Corresponding
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- Page 111 and 112: Lemma 6.2.3 Let 0 < s < s0 < 1, ρ
- Page 113 and 114: Bibliography [1] Albrecht, D.: Func
- Page 115 and 116: [54] Lunardi, A.: On the heat equat
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