Quasilinear parabolic problems with nonlinear boundary conditions

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Page 1 and 2:
Gutachter: Quasilinear parabolic pr
Page 3 and 4:
Contents 1 Introduction 3 2 Prelimi
Page 5 and 6:
Chapter 1 Introduction The present
Page 7 and 8:
to assume that m, c are bounded fun
Page 9 and 10:
We give now an overview of the cont
Page 11 and 12:
conditions of order ≤ 1. Sections
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Chapter 2 Preliminaries 2.1 Some no
Page 15 and 16:
Clearly, φA ∈ [0, π) and φA
Page 17 and 18:
Definition 2.2.3 Let X and Y be Ban
Page 19 and 20:
µ ∈ Σφα }. Let N ∈ N, Tj
Page 21 and 22:
We remark that a theorem of the Dor
Page 23 and 24:
Here f(A, ·) ∈ H0(Σ π 2 +η; B
Page 25 and 26:
Further, K ∞ (α, θa) := {a ∈
Page 27 and 28:
Using (2.19) for aω and bω yields
Page 29 and 30:
2.7 Evolutionary integral equations
Page 31 and 32:
Example 2.8.1 For J = [0, T ] and a
Page 33:
We conclude this section by illustr
Page 36 and 37:
kernel a. The operator B is inverti
Page 38 and 39:
x := f(0) ∈ X exists and we are l
Page 40 and 41:
with two positive constants C1, C2
Page 42 and 43:
with two positive constants C1 and
Page 44 and 45:
derivative theorem to this pair of
Page 46 and 47:
3.2 A general trace theorem Let X b
Page 48 and 49:
3.3 More time regularity for Volter
Page 50 and 51:
Theorem 3.4.2 Suppose X is a Banach
Page 52 and 53:
Our next objective is to show neces
Page 54 and 55:
Let u1 be the restriction of v1 to
Page 56 and 57:
Proof. We begin with the necessity
Page 59 and 60:
Chapter 4 Linear Problems of Second
Page 61 and 62:
The strategy for solving (4.1) is n
Page 63 and 64: Since ψj ≡ 1 on supp ϕj, we may
Page 65 and 66: Turning to (c), let g ∈ Ξi+1 and
Page 67 and 68: endowed with the norm | · | Y T 2
Page 69 and 70: We remark that the constant C2 stem
Page 71 and 72: One can then construct functions a
Page 73 and 74: analogous to (4.17), shows that S i
Page 75 and 76: Apply now V#, i+1 := I + k ∗ A#(
Page 77 and 78: Given a function v ∈ H 2 p(R n+1
Page 79 and 80: v is a solution of (4.40) on Ji+1 :
Page 81 and 82: Chapter 5 Linear Viscoelasticity In
Page 83 and 84: where δij denotes Kronecker’s sy
Page 85 and 86: problem ⎧ ⎪⎨ ⎪⎩ ∂tv −
Page 87 and 88: To see the converse direction, supp
Page 89 and 90: and up solves � Aup − ∆xup
Page 91 and 92: It can be written as where l(z, ξ)
Page 93 and 94: elongs to H∞ (Σ π 2 +η × Ση
Page 95 and 96: which allows us to write the first
Page 97 and 98: Chapter 6 Nonlinear Problems 6.1 Qu
Page 99 and 100: sufficiently small, say T ≤ T1
Page 101 and 102: (d) bD ∈ C(J0 × ΓD × U0), ∃C
Page 103 and 104: which entails (6.14). Corresponding
Page 105 and 106: substitution operators to be studie
Page 107 and 108: for all t, τ ∈ J, ξ, η ∈ K,
Page 109 and 110: to write where h2(t, τ, x) = h21(t
Page 111 and 112: Lemma 6.2.3 Let 0 < s < s0 < 1, ρ
Page 113: Bibliography [1] Albrecht, D.: Func
Page 117 and 118: kleines T mit Hilfe des Kontraktion
Page 119: Personal Details Curriculum Vitae N
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