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  • 1
    Electronic Resource
    Electronic Resource
    Das Verhalten der Ableitungen globaler Lösungen nichtlinearer Wellengleichungen für grosse Zeiten (1974)
    Springer
    Manuscripta mathematica 12 (1974), S. 197-204 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This note deals with the behavior of global classical solutions of a certain type of nonlinear wave-equations when t goes to infinity. Starting with results of Morawetz-Strauss [2] and of the author [3] about the time-decay rates for the spatial supremum of the soluion we estimate all its Sobolev-norms. Our main tools are estimates of the LP-decay rates for homogeneous wave-equations contained in a paper of von Wahl [5].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01168651
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  • 2
    Electronic Resource
    Electronic Resource
    LP-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II (1977)
    Springer
    Manuscripta mathematica 20 (1977), S. 227-244 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the global classical solvability of the Cauchy problem for nonlinear wave equations of higher order of the following form where Δ denotes the Laplacian, ζ a real constant, m a positive integer, and f the nonlinearity. Using results of the first part [6] concerning estimations for the kernel of the associated integral equation a priori estimates for certain LP-norms of the local regular solution are established for higher space dimensions and for a class of nonlinearities satisfying certain growth and positivity conditions. This leads to completely regular solutions by means of the Sobolev embedding theorems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01358638
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  • 3
    Electronic Resource
    Electronic Resource
    Time decay for nonlinear wave equations in two space dimensions (1982)
    Springer
    Manuscripta mathematica 38 (1982), S. 387-400 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The Cauchy Problem for the equation utt−Δu+|u|p−1u=0 (x∈ℝ2, t〉0, ρ〉1) is studied. Smooth Cauchy data is prescribed, and no smallness condition is imposed. For ρ〉5, it is shown that the maximum amplitude of such a wave decays at the expected rate t−1/2 as t→∞. For 1+√8〈ρ≦5, the maximum amplitude still decays, but at a slower rate. These results are then used to demonstrate the existence of the scattering operator when ρ〉ρo, where ρo is the root of the cubic equation ρ3-2ρ2-7ρ-8=0; thus ρo≅4.15.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01170934
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  • 4
    Electronic Resource
    Electronic Resource
    Time dependent nonlinear Schrödinger equations (1979)
    Springer
    Manuscripta mathematica 27 (1979), S. 125-157 
    Details
    ISSN: 1432-1785
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove the existence of global classical solutions of the Cauchy-problem for nonlinear Schrödinger equations u′+iAu+f(|u|2)u or u′+Au+if(|u|2)u respectively. We need various growth conditions on the nonlinearity f and some restrictions on the admissible space dimension n.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299292
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  • 5
    Electronic Resource
    Electronic Resource
    On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity (1993)
    Springer
    Mathematische Annalen 296 (1993), S. 215-234 
    Details
    ISSN: 1432-1807
    Keywords: 35A05 ; 35L20 ; 73F99
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01445103
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  • 6
    Electronic Resource
    Electronic Resource
    Self-similar and asymptotically self-similar solutions of nonlinear wave equations (2000)
    Springer
    Mathematische Annalen 316 (2000), S. 259-281 
    Details
    ISSN: 1432-1807
    Keywords: Mathematics Subject Classification (1991): 35L05, 35L70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002080050013
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  • 7
    Electronic Resource
    Electronic Resource
    Die Existenz regulärer Lösungen für Cauchy- und Anfangs-Randwertprobleme nichtlinearer Wellengleichungen (1974)
    Springer
    Mathematische Zeitschrift 140 (1974), S. 263-279 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214167
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  • 8
    Electronic Resource
    Electronic Resource
    Regulation of the synthesis of hydrogenase (formate hydrogen-lyase linked) of E. coli (1984)
    Springer
    Archives of microbiology 139 (1984), S. 299-304 
    Details
    ISSN: 1432-072X
    Keywords: Hydrogenase ; Regulatory mutants ; Formate hydrogen-lyase ; Escherichia coli ; hyd::lac fusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The regulation of synthesis of the hydrogenase which is a component of the formate hydrogen-lyase complex was studied by means of a strain of Escherichia coli possessing a transcriptional fusion of the hydrogenase gene (hyd) with the lacZ gene (hyd::lac fusion). Formation of active hydrogenase in the wild strain requires the presence of nickel in the medium; transcription of the hyd gene, however, is independent from the prescence of Ni2+. Ni2+ addition to Ni2+-prestarved cells did not lead to any activation of presumptive hydrogenase apoprotein. Regulatory mutants were isolated in which nitrate repression of hyd::lac expression was relieved. Two main classes of regulatory mutants were identified: (i) Mutants with a defect in nitrate reductase; (ii) mutants with a cis-dominant regulatory mutation closely linked to the hyd::lac fusion. In the presence of formate which acts as an inducer, the hyd::lac fusion was also expressed under aerobic conditions. The results infer that nitrate repression of transcription of the hydrogenase structural gene is not effected by nitrate itself but requires the function of the electron transport chain leading to nitrate and that mutations in the promoter/operator region of the hyd cistron may confer insensitivity to redox control both by oxygen and nitrate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00408370
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  • 9
    Electronic Resource
    Electronic Resource
    The seleno-polypeptide of formic dehydrogenase (formate hydrogen-lyase linked) from Escherichia coli: genetic analysis (1985)
    Springer
    Archives of microbiology 141 (1985), S. 359-363 
    Details
    ISSN: 1432-072X
    Keywords: Escherichia coli ; Phage Mu d, formic dehydrogenase ; Seleno-polypeptide ; Respiratory pathway
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract The site of integration of phage Mu d (Ap lac) in mutant M9s which leads to deficiency of formic dehydrogenase (benzylviologen-linked) activity was determined. It was shown that the phage had inserted into the gene for the seleno-polypeptide of the enzyme (80 kd) leading to the formation of a truncated peptide (60 kd) still able to incorporate Se. Synthesis of the truncated polypeptide is subject to the same regulatory signals as that of the wild-type enzyme. The formation of the 110 kd seleno-polypeptide, which is a constituent component of the formic dehydrogenase from the formate-nitrate respiratory pathway, is unimpaired in mutant M9s. The location of the gene for the 80 kd seleno-polypeptide was mapped at 92.4 min of the Escherichia coli chromosome.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00428850
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  • 10
    Electronic Resource
    Electronic Resource
    Expression of pyruvate formate-lyase of Escherichia coli from the cloned structural gene (1982)
    Springer
    Archives of microbiology 132 (1982), S. 365-371 
    Details
    ISSN: 1432-072X
    Keywords: Pyruvate formate-lyase ; Anaerobiosis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology
    Notes: Abstract It is shown here that a plasmid (p29) derived from the transducing phage λaspC2 (Christiansen and Pedersen 1981) codes for pyruvate formate-lyase. The identity of the 80 kilodaltons (kd) gene product of plasmid p29 with the pyruvate formate-lyase polypeptide was proven (i) by comigration of the gene product expressed in the maxicell system with purified enzyme on O'Farrell gels, and (ii) by comparison of the peptide maps obtained from limited proteolysis. In vivo the 80 kd form of the enzyme was proteolytically converted to a 78 kd polypeptide. The two polypeptides (80 kd and 78 kd) and their charge isomers present in purified enzyme preparations are therefore products of a single gene. Aerobically grown cells of Escherichia coli contained a basal level of pyruvate formate-lyase which was derepressed 5-to 10-fold under anaerobiosis. Derepression also occurred during anaerobic growth on glycerol plus fumarate. Presence of plasmid p29 caused overproduction of pyruvate formatelyase, 11-fold upon anaerobic growth on glucose, 14-fold upon aerobic growth on glucose and 33-fold upon aerobic growth at the expense of D-lactate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00413390
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