Quasilinear parabolic problems with nonlinear boundary conditions

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Erklärung Hiermit versichere ich, dass ich die vorliegende Arbeit selbstständig und ohne fremde Hilfe verfasst, keine anderen als die von mir angegebenen Quellen und Hilfsmittel benutzt und die den benutzten Werken wörtlich oder inhaltlich entnommenen Stellen als solche kenntlich gemacht habe. Halle (Saale), 07. Januar 2003 Rico Zacher
Personal Details Curriculum Vitae Name: Rico Zacher Date/Place of Birth: 04.12.1973, Weimar Nationality: German Marital Status: single Education 1980-1990 J.W. Goethe Polytechnic School, Weimar 1990-1991 Special Classes for Mathematics and Physics at Martin Luther University Halle 1991-1992 Georg Cantor Grammar School, Halle June 1992 A-Levels 1992-1993 military service, Strausberg (Berlin) 1993-1999 studies in mathematics (main subject) and physics (subsidiary subject), University Halle/S., Germany Sept. 1995-June 1996 visiting student, University College Cork in Ireland Jan. 1999 diploma, title of the diploma thesis: ’Persistent solutions for age-dependent pair-formation models’ since 1999 PhD student at the Department of Mathematics, Martin Luther University Halle-Wittenberg Awards/Prizes/Scholarships 1992 winner of the Federal Competition in Mathematics Oct. 1993-March 1999 scholarship from the ’Studienstiftung des deutschen Volkes’ Oct. 1999 Laudert Award of the Georg Cantor Organization Nov. 1999-March 2002 PhD scholarship from the ’Studienstiftung’ Participation in Conferences/Workshops/Summer Schools June 1998 Summer School in Besançon: ’Evolution Equations’ May 1999 Spring School in Paseky: ’Evolution Equations’ June 1999 Summer School in Besançon: ’Evolution Equations and Nonlinear Partial Differential Equations’ 28.06.-02.07.1999 Conference in Besançon: ’Nonlinear Partial Differential Equations’ 19.03.-25.03.2000 Conference in Oberwolfach: ’Functional Analysis and Partial Differential Equations’ 30.10.-04.11.2000 Conference in Trento: ’Evolution Equations 2000 and Appl. to Physics, Industry, Life Sciences and Economics’ 17.03.-23.03.2002 Workshop in Marrakesch: ’Semigroup Theory, Evolution Equations and Applications’ 01.12.-06.12.2002 Workshop in Wittenberg: ’Modelling and Analysis of Moving Boundaries’ Halle, 07 January 2003
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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
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 and 114: Bibliography [1] Albrecht, D.: Func
Page 115 and 116: [54] Lunardi, A.: On the heat equat
Page 117: kleines T mit Hilfe des Kontraktion
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Quasilinear parabolic problems with nonlinear boundary conditions

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