2015
DOI: 10.1007/s10231-015-0505-z
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$$L^1$$ L 1 – $$L^p$$ L p estimates for radial solutions of the wave equation and application

Abstract: It is well known that, for space dimension n > 3, one cannot generally expect L 1 -L p estimates for the solution ofwhere (t, x) ∈ R + × R n . In this paper, we investigate the benefits in the range of 1 ≤ p ≤ q such that L p -L q estimates hold under the assumption of radial initial data. In the particular case of odd space dimension, we prove L 1 -L q estimates for 1 ≤ q < 2n n−1 and apply these estimates to study the global existence of small data solutions to the semilinear wave equation with power nonline… Show more

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Cited by 4 publications
(3 citation statements)
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References 21 publications
(37 reference statements)
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“…Remark 1.4. The decay rate in (19) is the same as the decay rate of the linear problem, in (13), provided that u 1 is non-trivial (see Remark 1.3).…”
Section: 2mentioning
confidence: 98%
See 1 more Smart Citation
“…Remark 1.4. The decay rate in (19) is the same as the decay rate of the linear problem, in (13), provided that u 1 is non-trivial (see Remark 1.3).…”
Section: 2mentioning
confidence: 98%
“…as conjectured by Strauss [47], after that John proved it in space dimension n = 3 [31]. Several authors studied the problem in different space dimension, finding blow-up in finite time for a suitable choice of initial data in the subcritical range [24,30,44,46,52]), and global existence of small data solutions in the supercritical range [19,23,25,48,54]. The critical exponent of the Cauchy problem for the semilinear wave equation becomes Fujita exponent 1 + 2/n if a damping term u t is added to the equation in (7) (see [29,41,49,53]).…”
Section: Introductionmentioning
confidence: 96%
“…Starting from the general superstructure shown in Figure 8.1, the optimisation of the wastewater network has been solved by using the Branch-And-Reduce Optimisation Navigator-BARON solver in GAMS (Tawarmalani and Sahinidis, 2005). This solver was adopted because the bilinear terms (in Equations (8.2) and (8.7)) in the model cause it to be highly non-linear and to have multiple local optima whose presence calls for the application of global optimisation techniques (Liberti et al, 2006).…”
Section: Resultsmentioning
confidence: 99%