Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0830-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0830-1 | ||
| 245 | 0 | 0 | |a Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients |h [Elektronische Daten] |c [Claudia Garetto, Michael Ruzhansky] |
| 520 | 3 | |a In this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients. This means assuming that the coefficients are less regular than Hölder. The characteristic roots are also allowed to have multiplicities. For such equations, we describe the notion of a ‘very weak solution' adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifiers of coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or to ultradistributional solutions under conditions when such solutions also exist. In concrete applications, the dependence on the regularising parameter can be traced explicitly. | |
| 540 | |a The Author(s), 2014 | ||
| 700 | 1 | |a Garetto |D Claudia |u Department of Mathematical Sciences, Loughborough University, LE11 3TU, Loughborough, Leicestershire, UK |4 aut | |
| 700 | 1 | |a Ruzhansky |D Michael |u Department of Mathematics, Imperial College London, 180 Queen's Gate, SW7 2AZ, London, UK |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/1(2015-07-01), 113-154 |x 0003-9527 |q 217:1<113 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0830-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0830-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Garetto |D Claudia |u Department of Mathematical Sciences, Loughborough University, LE11 3TU, Loughborough, Leicestershire, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ruzhansky |D Michael |u Department of Mathematics, Imperial College London, 180 Queen's Gate, SW7 2AZ, London, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/1(2015-07-01), 113-154 |x 0003-9527 |q 217:1<113 |1 2015 |2 217 |o 205 | ||