We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order,which can degenerate,on a part of the boundary,on a segment in the interior of the domain and in t...We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order,which can degenerate,on a part of the boundary,on a segment in the interior of the domain and in time.展开更多
This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1...This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p <n + 2, and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 <m < 2 andnq + (n + 1)p < 2 +mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.展开更多
基金Project supported partially by NNSF of China Grant No.10171008NSF of Hunan Province Grant No.03JJY3003
文摘We deal with the existence of periodic solutions for doubly degenerate quasilinear parabolic equations of higher order,which can degenerate,on a part of the boundary,on a segment in the interior of the domain and in time.
基金This work was supported by the National Natural Science Foundation of China(Grant No.19831060)the"333"Project of Jiangsu Province.
文摘This paper is devoted to study the classification of self-similar solutions to the quasilinear parabolic equations with nonlinear gradient termsu t = Δ(u m) - uq∣Δu∣ p withm ≥ 1,p,q > 0 andp +q >m. Form = 1, it is shown that the very singular self-similar solution exists if and only ifnq + (n +1)p <n + 2, and in case of existence, such solution is unique. Form > 1, it is shown that very singular self-similar solutions exist if and only if 1 <m < 2 andnq + (n + 1)p < 2 +mn, and such solutions have compact support if they exist. Moreover, the interface relation is obtained.
