The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtai...The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.展开更多
The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equ...The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equation ut = △um-uq, m > 0, q > 0 and the p-Laplace equation ut = div(|△u|p-2△u)-uq, P > 1, q > 0. In particular, as an application of the results, the necessary and sufficient condition for the solutious of the above p-Laplace equation with nonnegative finite Borel measures as initial conditions to have the instantaneous shrinking property of the support is obtained. This is an answer to an open problem posed by R. Kersner and A. Shishkov.展开更多
The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is...The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.展开更多
基金supported by the Fujian Provincial Natural Science Foundation of China (No. Z0511048)
文摘The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.
基金the Teching and Research Award Fund for Outstanding Young Teachers inHigher Education Institutions of MOE, China (No.[2000]26)
文摘The aim of this paper is to discuss the instantaneous shrinking and localization of the support of functions in Yλ(m,p,q,N) and their applications to some nonlinear parabolic equations including the porous medium equation ut = △um-uq, m > 0, q > 0 and the p-Laplace equation ut = div(|△u|p-2△u)-uq, P > 1, q > 0. In particular, as an application of the results, the necessary and sufficient condition for the solutious of the above p-Laplace equation with nonnegative finite Borel measures as initial conditions to have the instantaneous shrinking property of the support is obtained. This is an answer to an open problem posed by R. Kersner and A. Shishkov.
文摘The relation between the global attractors Aε for a calss of quasilinear parabolic equations and the global attractor A0 for the homogenized equation is discussed, and an explicit error estimate between Aε and A0 is given.
