Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong...The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(-) is permitted to have zero measure. In particular, the existence of interfaces of solutions is obtained.展开更多
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Cle...The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ＇（.） is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].展开更多
文摘Under some conditions, one seows that the generalized solutions of the first boundary value problem for the equation [GRAPHICS] have the property of finite speed of propagation.
基金Project supported by the Teaching and Research Award Found for Outstanding Young Teachers in Higher Education Institutions of MOE ([2000]26)China and the NNSF (1001015) of China
文摘The aim of this paper is to discuss the Cauchy problem for quasilinear degenerate parabolic equations of the formwhere φ∈C1(R1) is a strictly monotonically increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ'(-) is permitted to have zero measure. In particular, the existence of interfaces of solutions is obtained.
基金Project supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE(No.[2000]26)the 973 Project of the Ministry of Science and Technology of China(No.2006CB805902)+1 种基金the National Natural Science Foundation of China(No.10571072)the Key Laboratory of Symbolic Computation and Knowledge Engineering of the Ministry of Education of China and the 985 Project of Jilin University.
文摘The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form： μt-△φ（μ） = 0 ,where φ ε C1（R^1） is a strictly monotone increasing function. Clearly, the above equation has strong degeneracy, i.e., the set of zero points of φ＇（.） is permitted to have zero measure. This is an answer to an open problem in [13, p. 288].
