Periodic solutions of parabolic-elliptic obstacle problems (Q1813576)

The authors investigate the periodic behaviour of the solutions to a special parabolic-elliptic obstacle problem in \(R\). Under suitable periodicity conditions on the data, they give an existence and uniqueness theorem for periodic solutions, which is asymptotically stable and it is characterized by global boundedness of the trajectory. The methods are the same as in a previous paper [e.g.: Pitman Res. Notes Math. Ser. 208, 68-76 (1989; Zbl 0696.35006); J. Math. Soc. Japan 41, No. 4, 625-640 (1989; Zbl 0667.35077; Zbl 0685.35104)], however, here a further difficulty arises from the presence of the obstacle. A new regularity result is obtained also.