Electron. J. Diff. Equ., Vol. 2011 (2011), No. 92, pp. 1-30.

Time-dependent domains for nonlinear evolution operators and partial differential equations

Chin-Yuan Lin

Abstract:
This article concerns the nonlinear evolution equation
$$\displaylines{ \frac{du(t)}{dt} \in A(t)u(t), \quad 0 \leq s < t < T, \cr u(s) = u_0 }$$
in a real Banach space X, where the nonlinear, time-dependent, and multi-valued operator $ A(t) : D(A(t)) \subset X \to X$ has a time-dependent domain D(A(t)). It will be shown that, under certain assumptions on A(t), the equation has a strong solution. Illustrations are given of solving quasi-linear partial differential equations of parabolic type with time-dependent boundary conditions. Those partial differential equations are studied to a large extent.

Submitted June 15, 2011. Published July 18, 2011.
Math Subject Classifications: 47B44, 47H20, 35J25, 35K20.
Key Words: Dissipative operators; evolution equations; parabolic and elliptic equations.

Show me the PDF file (387 KB), TEX file, and other files for this article.

Chin-Yuan Lin
Department of Mathematics
National Central University
Chung-Li 320, Taiwan
email: cylin@math.ncu.edu.tw

Return to the EJDE web page