A semilinear parabolic system with a free boundary

作者：Wang Mingxin^*; Zhao Yonggang

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2015, 66(6): 3309-3332.

DOI：10.1007/s00033-015-0582-2

• Parabolic system
• Free boundary
• Regularity
• Global existence
• Blowup
• Long-time behavior

This paper deals with a semilinear parabolic system with reaction terms and a free boundary in one space dimension, where evolves according to the free boundary condition s' (t) = -mu(u(x) vertical bar rho v(x)) . The main aim of this paper was to study the existence, uniqueness, regularity and long-time behavior of positive solution (maximal positive solution). Firstly, we prove that this problem has a unique positive solution when p, q >= 1 , and a (unique) maximal positive solution when p < 1 or q < 1. Then, we study the regularity of and . At last, we discuss the global existence, finite-time blowup of the unique positive solution (maximal positive solution) and long-time behavior of bounded global solution.

• 出版日期2015-12
• 单位哈尔滨工业大学