This article concerns the nonlinear evolution equation
in a real Banach space X, where the nonlinear, time-dependent, and multi-valued operator 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.
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| Chin-Yuan Lin |
Department of Mathematics
National Central University
Chung-Li 320, Taiwan
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