Bassanini, Piero:
Su un teorema di unicità per l'equazione semilineare del calore in un dominio illimitato
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Serie 8 78 (1985), fasc. n.6, p. 278-285, (Italian)
pdf (709 Kb), djvu (688 Kb). | MR 0919020 | Zbl 0656.35064
Sunto
A periodic BVP for a semilinear elliptic-parabolic equation in an unbounded domain $\Omega$ contained in a half-space of $\mathbb{R}^{n}$ is considered, with Dirichlet boundary conditions on the finite part of $\partial \Omega$. A theorem of uniqueness of periodic solutions is proved by showing that a suitable function of the "energy" $E(x)$ is subharmonic in $\Omega$ and satisfies a Phragmèn-Lindelöf growth condition at infinity.
Referenze Bibliografiche
[2]
G. PRODI (
1952) -
Soluzioni periodiche di equazioni a derivate parziali di tipo parabolico non lineari, «
Riv. Mat. Univ. Parma»,
3, 265-290. |
MR 55543 |
Zbl 0049.07502[3]
I.I. SHMULEV (
1961) -
Periodic solutions of boundary value problems without initial conditions for parabolic equations, «
Dokl. Akad. Nauk SSSR»,
141, 1313-1316. |
MR 132902 |
Zbl 0154.36103[4]
P. FIFE (
1964) -
Solutions of parabolic boundary value problems existing for all times, «
Arch. Rat. Mech. Anal.»,
16, 155-186. |
MR 167727 |
Zbl 0173.38204[5]
C. VAGHI (
1972) -
Soluzioni limitate o quasiperiodiche dell'equazione quasi lineare del calore, «
Rend. Sem. Mat. Fis. Milano»,
42, 25-46. |
MR 333448 |
Zbl 0328.35047[6]
B.-P. LIU e
C.V. PAO (
1982) -
Periodic solutions of coupled semilinear parabolic boundary value problems, «
Nonlinear Anal.»,
6, 237-252. |
fulltext (doi) |
MR 654316 |
Zbl 0499.35012[7]
O. VEJVODA (
1966) -
Periodic solutions of nonlinear partial differential equations of evolution,
Equadiff II (Conf. Bratislava, 1966), 293-300. |
fulltext EuDML |
MR 249793 |
Zbl 0183.10401[10]
A.N. TIHONOV e
A.A. SAMARSKII (
1963) -
Equations of Mathematical Physics,
Macmillan. |
MR 165209[11] N. CURLE e H.J. DAVIES (1968) - Modem Fluid Dynamics, Van Nostrand.
[12]
M.H. PROTTER e
H.F. WEINBERGER (
1967) -
Maximum principles in differential equations,
Prentice-Hall. |
MR 219861 |
Zbl 0153.13602[13]
D. GRAFFI (
1980) -
Nonlinear partial differential equations in physical problems,
Pitman. |
MR 580946 |
Zbl 0453.35001