Local and global smoothing effects for some linear hyperbolic equations with a strong dissipation
By Marina Ghisi, Massimo Gobbino, Alain Haraux. 2014
53 citations recorded by the source corpus.
We consider an abstract second order linear equation with a strong dissipation, namely a friction term which depends on a power of the “elastic” operator. In the homogeneous case, we investigate the phase spaces in which the initial value problem gives rise to a semigroup, and the further regularity of solutions. In the nonhomogeneous case, we study how the regularity of solutions depends on the regularity of forcing terms, and we characterize the spaces where a bounded forcing term yields a bounded solution. What we discover is a variety of different regimes, with completely different behaviors, depending on the exponent in the friction term. We also provide counterexamples in order to show the optimality of our results. Mathematics Subject Classification 2010 (MSC2010): 35L10, 35L15, 35L20.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1b2012bd69082e82ee7ffc23ba9c4d3c1cb11f58
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In Applied Mathematics
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Citations in the corpus
- A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations (2017, background): “In particular, we address the interested reader to [21], where smoothing e ff ect are investigated in abstract setting, in bounded domains.”
- A classification of structural dissipations for evolution operators (2016, background): “[26], where the influence from the regularity of the data space on the regularity of the solution to structurally damped models is discussed, for any ı 0, in abstract setting.”