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Large data solutions for semilinear higher order equations
Dipartimento interateneo di Fisica, Università degli Studi di Bari, Via Orabona 4 70125 Bari, Italy |
$ u_{tt}+ (-\Delta)^{2\theta}u+2\mu(-\Delta)^\theta u_t + |u|^{p-1}u = 0, \quad t\geq0, \ x\in {\mathbb{R}}^n, $ |
$ \mu>0 $ |
$ \theta>0 $ |
References:
[1] |
M. D'Abbicco and M. R. Ebert,
A classification of structural dissipations for evolution operators, Math. Methods Appl. Sci., 39 (2016), 2558-2582.
doi: 10.1002/mma.3713. |
[2] |
M. D'Abbicco and M. R. Ebert,
A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations, Nonlinear Analysis, 149 (2017), 1-40.
doi: 10.1016/j.na.2016.10.010. |
[3] |
M. D'Abbicco and S. Lucente, The beam equation with nonlinear memory, Zeitschrift fur Angewadte Mathematik und Physik, 67 (2016), Art. 60, 18 pp.
doi: 10.1007/s00033-016-0655-x. |
[4] |
M. D'Abbicco, M. R. Ebert and S. Lucente,
Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation, Math Meth Appl Sci., 40 (2017), 6480-6494.
doi: 10.1002/mma.4469. |
[5] |
H. Hajaiej, X. Yu and Z. Zhai,
Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms, Journal of Mathematical Analysis and Applications, 396 (2012), 569-577.
doi: 10.1016/j.jmaa.2012.06.054. |
[6] |
S. Lucente,
Critical exponents and where to find them, Bruno Pini Mathematical Analysis Seminar, 9 (2018), 102-114.
|
[7] |
T. D. Pham, M. Kinane and M. Reissig,
Global existence for semi-linear structurally damped $\sigma$-evolution models, J. Math. Anal. Appl., 431 (2015), 569-596.
doi: 10.1016/j.jmaa.2015.06.001. |
[8] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006.
doi: 10.1090/cbms/106. |
show all references
References:
[1] |
M. D'Abbicco and M. R. Ebert,
A classification of structural dissipations for evolution operators, Math. Methods Appl. Sci., 39 (2016), 2558-2582.
doi: 10.1002/mma.3713. |
[2] |
M. D'Abbicco and M. R. Ebert,
A new phenomenon in the critical exponent for structurally damped semi-linear evolution equations, Nonlinear Analysis, 149 (2017), 1-40.
doi: 10.1016/j.na.2016.10.010. |
[3] |
M. D'Abbicco and S. Lucente, The beam equation with nonlinear memory, Zeitschrift fur Angewadte Mathematik und Physik, 67 (2016), Art. 60, 18 pp.
doi: 10.1007/s00033-016-0655-x. |
[4] |
M. D'Abbicco, M. R. Ebert and S. Lucente,
Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation, Math Meth Appl Sci., 40 (2017), 6480-6494.
doi: 10.1002/mma.4469. |
[5] |
H. Hajaiej, X. Yu and Z. Zhai,
Fractional Gagliardo-Nirenberg and Hardy inequalities under Lorentz norms, Journal of Mathematical Analysis and Applications, 396 (2012), 569-577.
doi: 10.1016/j.jmaa.2012.06.054. |
[6] |
S. Lucente,
Critical exponents and where to find them, Bruno Pini Mathematical Analysis Seminar, 9 (2018), 102-114.
|
[7] |
T. D. Pham, M. Kinane and M. Reissig,
Global existence for semi-linear structurally damped $\sigma$-evolution models, J. Math. Anal. Appl., 431 (2015), 569-596.
doi: 10.1016/j.jmaa.2015.06.001. |
[8] |
T. Tao, Nonlinear Dispersive Equations: Local and Global Analysis, CBMS Regional Conference Series in Mathematics, 106. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2006.
doi: 10.1090/cbms/106. |
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