TY  - JOUR
AB  - The present article is concerned with the Lyapunov stability of stationary solutions to the Allen-Cahn equation with a strong irreversibility constraint, which was first intensively studied in [2] and can be reduced to an evolutionary variational inequality of obstacle type. As a feature of the obstacle problem, the set of stationary solutions always includes accumulation points, and hence, it is rather delicate to determine the stability of such non-isolated equilibria. Furthermore, the strongly irreversible Allen-Cahn equation can also be regarded as a (generalized) gradient flow; however, standard techniques for gradient flows such as linearization and Łojasiewicz-Simon gradient inequalities are not available for determining the stability of stationary solutions to the strongly irreversible Allen-Cahn equation due to the non-smooth nature of the obstacle problem.
AU  - Akagi, G.*
AU  - Efendiyev, M.A.
C1  - 72907
C2  - 56783
CY  - Edinburgh Bldg, Shaftesbury Rd, Cb2 8ru Cambridge, England
TI  - Lyapunov stability of non-isolated equilibria for strongly irreversible Allen-Cahn equations.
JO  - Proc. R. Soc. Edinburgh, Sect. A
PB  - Cambridge Univ Press
PY  - 2024
SN  - 0308-2105
ER  - 

TY  - JOUR
AB  - We study a model of ferromagnetic material with hysteresis effects. The magnetic moment behaviour is described by the nonlinear Landau-Lifshitz equation with an additional term modelling the hysteresis. This term takes the form of a maximal monotone operator acting on the time derivative of the magnetic moment. In our model, it is approximated via a relaxing heat equation. For this relaxed model we prove local existence of regular solutions.
AU  - Carbou, G.*
AU  - Efendiyev, M.A.
AU  - Fabrie, P.*
C1  - 1266
C2  - 26982
SP  - 759-773
TI  - Relaxed model for the hysteresis in micromagnetism.
JO  - Proc. R. Soc. Edinburgh, Sect. A
VL  - 139
IS  - 4
PB  - Royal Soc Edinburgh
PY  - 2009
SN  - 0308-2105
ER  - 

TY  - JOUR
AU  - Walcher, S.
C1  - 21360
C2  - 19476
SP  - 633-649
TI  - Plane polynomial vector fields with prescribed invariant curves.
JO  - Proc. R. Soc. Edinburgh, Sect. A
VL  - 130A
PY  - 2000
SN  - 0308-2105
ER  - 

TY  - JOUR
AB  - Parsley (Petroselinum crispum L.) is known to respond to pathogen attack by the synthesis of furanocoumarins and to UV-irradiation by the synthesis of flavone glycosides, whereas ozone treatment results in the induction of both pathways. Ozone treatment (200 nl 1−1, 10 h) of parsley seedlings results in an increased mRNA level of early genes within 3 h [pathogenesis related proteins PR1, PR2 and an elicitor-induced protein with unknown function (Eli 16)], of intermediate induced genes within 6 h [phenylalanine ammonia-lyase (PAL), 4-coumaroyl-CoA ligase (4CL), chalcone synthase (CHS)], and of late genes within 12 h [hydroxyproline-rich glycoprotein (HRGP), peroxidase (POD)]. 2D-PAGE of in vitro translated poly(A)+ RNA isolated from ozone-treated parsley seedlings revealed about 20 induced and 10 repressed translation products. A cDNA library from parsley seedlings was differential screened, yielding several induced cDNA clones. One of the ozone-induced cDNA clones could be identified as coding for PR1-1 by hybrid-selected in vitro translation and by DNA sequence analysis.
AU  - Eckey-Kaltenbach, H.
AU  - Großkopf, E.*
AU  - Sandermann, H.
AU  - Ernst, D.
C1  - 46494
C2  - 0
SP  - 63-74
TI  - Induction of pathogen defence genes in parsley (Petroselinum crispim L.) plant by ozone.
JO  - Proc. R. Soc. Edinburgh, Sect. A
VL  - 102
PY  - 1994
SN  - 0308-2105
ER  -