-
Abstract
The present article consists of two parts. In the first part we
consider evolutionary variational inequalities with a nonlinearity which is
described by a differential inclusion. Using the frequency-domain method
we prove, under certain assumptions, the dissipativity of our
variational inequality which is important for the asymptotic
behavior of the system. In the second part a coupled system of Maxwell's
equation and the heat equation is considered. For this system we introduce
the notion of stability on a finite-time interval and present a theorem
on this type of stability.
Mathematics Subject Classification: Primary: 35B35, 35B40; Secondary: 35K15, 35L20, 80A20.
\begin{equation} \\ \end{equation}
-
References
[1]
|
G. Duvant and J.L. Lions, "Inequalities in Mechanics and Physics," Springer - Verlag, Berlin, 1976.
|
[2]
|
D. Kalinichenko, V. Reitmann and S. Skopinov, Stability and bifurcations in a finite time interval on variational inequalities, Differential Equations, 48, no. 13 (2012), 1-12.
|
[3]
|
Y. Kalinin, V. Reitmann and N. Yumaguzin, Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect, Discrete and Continuous Dynamical Systems - Supplement 2011, 2 (2011), 754-762.
|
[4]
|
A.L. Likhtarnikov and V.A. Yakubovich, The frequency theorem for equations of evolutionary type, Siberian Math. J., 17 (1976), 790-803.
|
[5]
|
R.V. Manoranjan, H.M. Yin and R. Showalter, On two-phase Stefan problem arising from a microwave heating process, Contin. and Discrete Dynamical Systems, Serie A, 15 (2006), 1155-1168.
|
[6]
|
A.N. Michel and D.W. Porter, Practical stability and finite-time stability of discontinuous systems, IEEE Trans. Circuit Theory, 19 (1972), 123-129.
|
[7]
|
A.A. Pankov, "Bounded and Almost Periodic Solutions of Nonlinear Differential Operator Equations," Naukova Dumka, Kiev, 1986 (in Russian).
|
[8]
|
H. Triebel, "Interpolation Theorie, Function Spaces, Differential Operators," Amsterdam, North-Holland, 1978.
|
[9]
|
L. Weiss and E.F. Infante, On the stability of systems defined over a finite time interval, Proc. Nat. Acad. Sci., U.S.A., 54 (1965), 44-48.
|
-
Access History