Multiplicity results for interfaces of Ginzburg–Landau–Allen–Cahn equations in periodic media
نویسندگان
چکیده
منابع مشابه
Multiplicity of periodic solutions in bistable equations
We study the number of periodic solutions in two first-order non-autonomous differential equations, both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in a time-varying external magnetic field. When the amplitude of the external field is increased, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite ...
متن کاملglobal results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Motion of discrete interfaces in low-contrast periodic media
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional low-contrast periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and a discrete-to-continuum analysis. As in a recent paper by Braides and Scilla dealing with high-contrast periodic media, we give an example showing that in general the effective motion...
متن کاملMultiplicity results for some nonlinear Schrödinger equations with potentials
(K1) K ∈ C(R), K is bounded and K(x) > 0 ∀ x ∈ R. One seeks solutions uε of (NLS) that concentrate, as ε→ 0, near some point x0 ∈ R (semiclassical standing waves). By this we mean that for all x ∈ R \ {x0} one has that uε(x) → 0 as ε→ 0. When K equals a positive constant, say K(x) ≡ 1, (NLS) has been widely investigated, see [2, 3, 10, 12, 15, 16, 18] and references therein. Moreover, the exist...
متن کاملMultiplicity of Periodic Solutions for Differential Equations Arising in the Study of a Nerve Fiber Model
We deal with the periodic boundary value problem for a second-order nonlinear ODE which includes the case of the Nagumo type equation vxx−gv+n(x)F (v) = 0, previously considered by Grindrod and Sleeman and by Chen and Bell in the study of the model of a nerve fiber with excitable spines. In a recent work we proved a result of nonexistence of nontrivial solutions as well as a result of existence...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2007
ISSN: 0001-8708
DOI: 10.1016/j.aim.2007.03.013