Rionero, Salvatore:
Asymptotic Behaviour of Solutions to a Nonlinear Third Order P.D.E. Modeling Physical Phenomena
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.3, p. 451-468, (English)
pdf (303 Kb), djvu (135 Kb). | MR 3051732 | Zbl 1282.35073
Sunto
The longtime behaviour of the solutions to the initial boundary value problem (1.1)-(1.3) modeling various physical phenomena, either in the autonomous case or in the nonautonomous case, is studied. Conditions guaranteeing ultimately boundedness and conditions guaranteeing nonlinear asymptotic global stability of the null solution are obtained. Boundary conditions, different from (1.2)1-(1.2)2, are also considered (Section 9).
Referenze Bibliografiche
[1]
P. MARCATI,
Abstract stability theory and applications to hyperbolic equations with time dependent dissipative force fields.
Comp. and Math. with Appl.,
12A (
1986), 541. |
MR 841985 |
Zbl 0604.35049[3] A. BARONE - G. PATERNÓ, Physics and Applications of the Josephson Effect. Wiley-Interscience, New York (1982).
[4]
B. D. JOSEPHSON,
Possible new effects in superconductive tunneling.
Phys. Lett. 1 (
1962), 251-253,
The discovery of tunneling supercurrents,
Rev. Mod. Phys B,
46 (
1974), 251-254 and the references therein. 1447, (2000). |
Zbl 0103.23703[5] P. S. LOMDHAL - O. H. SOERSEN - P. L. CHRISTIANSEN, Soliton Excitations in Josephson Tunnel Junctions. Phys. Rev. B 25 (1982), 5737-5748.
[6]
R. D. PARMENTIER,
Fluxons in Long Josephson Junctions. In:
Solitons in Action Proceedings of a workshop sponsored by the Mathematics Division, Army Research Office held at Redstone Arsenal, October 26-27, 1977 (Eds
Karl Lonngren and
Alwyn Scott).
Academic Press, New York, (
1978). |
MR 641555[7]
A. MORRO -
L. E. PAYNE -
B. STRAUGHAN,
Decay, growth, continuous dependence and uniqueness results in generalized heat conductions theories,
Appl. Anal.,
38, n. 4 (
1990), 231-243. |
fulltext (doi) |
MR 1116182 |
Zbl 0694.35007[8]
H. LAMB,
Hydrodynamics,
Cambridge University Press, Cambridge (
1959). |
MR 1317348[9]
R. NARDINI,
Soluzione di un problema al contorno della magneto-idrodinamica,
Ann. Mat. Pura Appl.,
35 (
1953), 269-290 (in italian). |
fulltext (doi) |
MR 63932 |
Zbl 0051.23801[10]
D. D. JOSEPH -
M. RENARDY -
J. C. SAUT,
Hyperbolicity and change of type in the flow of viscoelastic fluids,
Arch. Rational Mech. Anal.,
87 (
1985), 213-251. |
fulltext (doi) |
MR 768067 |
Zbl 0572.76011[11]
J. A. MORRISON,
Wave propagations in rods of Voigt material and visco-elastic materials with three-parameters models,
Quart. Appl. Math.,
14 (
1956), 153-169. |
fulltext (doi) |
MR 78848 |
Zbl 0071.39902[13]
B. D'ACUNTO -
A. D'ANNA,
Stability for a third order Sine-Gordon equation,
Rend. Math. Serie VII,
18 (
1998), 347-365. |
MR 1659822 |
Zbl 0921.35019[14]
A. D'ANNA -
G. FIORE,
Stability and attractivity for a class of dissipative phenomena.
Rend. Met. Serie VII, vol
21 (
2000), 191-206. |
MR 1884942 |
Zbl 1052.35036[15]
A. D'ANNA -
G. FIORE,
Global Stability properties for a class of dissipative phenomena via one or several Liapunov functionals,
Nonlinear Dyn. Sys. Theory,
5 (
2005), 9-38. |
MR 2163509 |
Zbl 1076.35015[16]
A. D'ANNA -
G. FIORE,
Stability Properties for Some Non-autonomous Dissipative Phenomena Proved by Families of Liapunov functionals,
Nonlinear Dyn. Sys. Theory,
9, n. 3 (
2009), 249-262. |
MR 2895584 |
Zbl 1195.35047[17]
S. RIONERO,
A rigorous reduction of the $L^2$-stability of the solutions to a nonlinear binary reaction-diffusion system of O.D.Es to the stability of the solutions to a linear binary system of O.D.Es.
J.M.A.A.,
310 (
2006), 372-392. |
fulltext EuDML |
fulltext (doi) |
MR 2227911[18]
J. N. FLAVIN -
S. RIONERO, Cross-diffusion influence on the nonlinear $L^2$-
stability analysis for a Lotka-Volterra reaction-diffusion system of P.D.Es.,
IMA J.Appl. Math.,
72, n. 5 (
2007), 540-555. |
fulltext (doi) |
MR 2361568 |
Zbl 1160.35032[19]
D. R. MERKIN,
Introduction to the theory of stability.
Springer text in Appl. Math V.
24 (
1997). |
MR 1418401[20]
J. N. FLAVIN -
S. RIONERO,
Qualitative estimates for Partial Differential Equations: an introduction. Boca Raton, Florida:
CRC Press, (
1996). |
MR 1396085 |
Zbl 0862.35001[21]
S. RIONERO,
Stability-Instability criteria for non-autonomous systems,
Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei, s.
9, Mat. Appl.,
20, n. 4 (
2009), 347- 367. |
fulltext (doi) |
MR 2550850 |
Zbl 1188.34067[23]
S. ZHENG,
Nonlinear Evolution Equations.
Monographs and Surveys in Pure Applied Mathematics,
133,
Chapman-Hall/CRC, (
2004). |
fulltext (doi) |
MR 2088362
Con il contributo del Ministero per i Beni e le Attività Culturali