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In this paper, we first establish a kind of weighted space-time L2 estimate, which belongs to Keel–Smith–Sogge-type estimates, for perturbed linear elastic wave equations. This estimate refines the corresponding one established by the second author [D. Zha, Space-time L2 estimates for elastic waves and applications, J. Differential Equations 263 2017, 4, 1947–1965] and is proved by combining the methods in the former paper, the first author, Wang and Yokoyama’s paper [K. Hidano, C. Wang and K. Yokoyama, On almost global existence and local well posedness for some 3-D quasi-linear wave equations, Adv. Differential Equations 17 2012, 3–4, 267–306] and some new ingredients. Then, together with some weighted Sobolev inequalities, this estimate is used to show a refined version of almost global existence of classical solutions for nonlinear elastic waves with small initial data. Compared with former almost global existence results for nonlinear elastic waves due to John [F. John, Almost global existence of elastic waves of finite amplitude arising from small initial disturbances, Comm. Pure Appl. Math. 41 1988, 5, 615–666] and Klainerman and Sideris [S. Klainerman and T. C. Sideris, On almost global existence for nonrelativistic wave equations in 3D, Comm. Pure Appl. Math. 49 1996, 307–321], the main innovation of our result is that it considerably improves the amount of regularity of initial data, i.e., the Sobolev regularity of initial data is assumed to be the smallest among all the admissible Sobolev spaces of integer order in the standard local existence theory. Finally, in the radially symmetric case, we establish the almost global existence of a low regularity solution for every small initial data in H3×H2.

. Τ(μ): 42. 35l: 52. 1A: 52. {/ ̂ s,}, {/ < g}, {/ = g}, {/ ̂ flr}, '}: 137. = <?(21):56;<ί!*: 60. , //(ω)Α*(<ίω), //(ω)^(ω): 57, 60, 64, 70, 236. J/ ̂ : 81. /+, /'r 64. ^p(/): 71, 80. J2?POM): 73, 74; Z^(/i): 79, 80. Um sup -4«, lim inf ^4n: 76. «-»· oo n-»· oo « μ: 89. //-Hm: 97. n-*· oo Π i = Ωι Χ ... χ Ωη: 112;< = i Π ^<: 158 ( i Mengen). 21, = 2li <8> ... (8)51«: 112; ι <8> 21<: 158 (21< σ-Algebren). iel μι = μι ® · · · <8» /«η: 116, 120; L <8> Ρ«: 162 (/*< Ma e, Ρ, W- iel Ma e). (A, 21«,^): 121; 162. (g) -ϊι: 163 (Xt Abbildungen, » e / Zufallsvariable). ||μ

Zeitgenossen). 31 l—25: M. HORNSCHUH, Das Leben des Origenes und die Entstehung der alexandrinischen Schule. 35 l, 52—78: ED. STOM- MEL f, Bischofsstuhl und hoher Thron (zu Paul von Samosata). 2,90—114:K.THRAEDE, Beiträge zur Datierung Commodians. e) Montanismus. Monarchianer. f) Konstantin und seine Zeit. Der trinitarische Streit. Donatismus. 9 3, 171—195: H. CHADWICK, Faith and Order at the Council of Nicaea: a note on the background of the sixth canon. 15 3, 1/2, 138—145: H. H. OLIVER, The epistle of Eusebius to Carpianus. Textual tradition and translation. 26 7, 497

total energy associated to a planar magnetoelastic wave motion in an electric disper- sive medium. As a last result of our work, we present the existence and uniqueness of an abstract Klein–Gordon functional wave equation by means of Hilbert space techniques. Keywords. Hilbert abstract methods for wave equation. 2000 Mathematics Subject Classification. 35L90, 35L05, 35L52. 1 Introduction One important topic of mathematical methods for wave propagation physics [1, 7] is to devise functional analytic techniques useful to implement approximate nu- merical schemes [8

> 9. Fully deprotonated Lys, L, coordinates to metal ions essentially as a substituted Gly (79M). 3.1 Stability Constants of Proton Complexes Protonation steps for Lys at the E- and a-amino groups are not completely separated. In terms of the first and second protonations, Lys with the deprotonated a-amino and protonated &-amino groups predominates over Lys with the protonated a-amino and deprotonated &-amino groups (79M). The stability constants of the proton complexes of Lys hitherto reported are summarized in Table 4. Early data (30SA,35L,52A,53P) were

Analyseperspektive 21 l ,3. Lesen im Text der Fremde 24 1.3.l. Der Leseprozeß und die Autorfiktion 24 1.3.2. Bausteine der Subjektivität 28 l .4. Zwischen Vermitteln und Anpassen: der Rezipient als Übersetzer 31 1.5, Innovative und kreative Aspekte der Rezeption 34 1.5.1. Zwischen Normwandel und Normbestätigung 35 l .5.2. Innovative und kreative Rezeption 37 1.5.3. Das Problem der Innovationstoleranz 39 2. Reiseberichte 40 2.1. In der Fremde daheim 45 2. l. l . Erwartungsaffekte 45 2. l .2, Vorurteile oder Orientierungshilfen 48 2.1.3. Wahrnehmungsweisen: Alterität, Alienität und

- geben54). m ) Zwischenentscheidungen: Zwischenentscheidungen über Streitpunkte, bei denen es sich um Elemente des sachlichen Anspruchs selbst handelt, sind 4S) Barnstedt DNotZ 1958, 470. 49) Länge-Wulff HöfO Rn. 361 S. 481; vgl. nachstehend unter „Streitgenossen- schaft". 50) Baur FGG § 14 II. 51) OLG Hamm 29. 5.1956 - 10 Wlw. 59/56 - RdL 1959, 240 (RdL 1957, 56, Z 35, L). 52) Baur FGG § 14 I 2; Wöhrmann-Herminghausen LwVG § 14, Anm. 14, 15; Barnstedt RdL 1959 S. 144 (145), BGH 9.10.1951 - V BLw. 30/50 - RdL 1952 S. 17; Länge-Wulff LwVG zu § 22 D VI 1 f