Approximate Controllability of a Semilinear System Involving a Fully Nonlinear Gradient Term

作者：Du, Runmei; Wang, Chunpeng^*; Zhou, Qian

来源：Applied Mathematics and Optimization, 2014, 70(1): 165-183.

DOI：10.1007/s00245-014-9238-4

• Approximate controllability
• Degenerate equation
• Gradient term

This paper concerns a control system governed by a semilinear degenerate equation involving a fully nonlinear gradient term. The equation may be weakly degenerate and strongly degenerate on a portion of the lateral boundary, and the gradient term can be controlled by the diffusion term. The linearized system is shown to be approximately controllable by constructing a control by means of its conjugate problem. By doing a series of precise compactness estimates, we prove that the semilinear system is approximately controllable.

• 出版日期2014-8
• 单位吉林大学