The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u wi...The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u with r>0.展开更多
It is proved that the vortices of a Ginzburg-Landau system are attracted by impurities or inhomogeneities in the super-conducting materials. The strong H1-convergence for the system is also studied.
Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appro...Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals.展开更多
We obtain the H1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a c...We obtain the H1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution in the evolution of harmonic maps.展开更多
基金supported by the National Natural Sciences Foundation of China (No.19701018).
文摘The homogenization of the nonlinear degenerate parabolic equations, diva(x/ε,t/ε,u,u)=f(x,t) is studied, where a(y,t,μ,λ) is periodic in (y,t) and b may be a nonlinear function whose prototype is |μ|~r sign u with r>0.
文摘It is proved that the vortices of a Ginzburg-Landau system are attracted by impurities or inhomogeneities in the super-conducting materials. The strong H1-convergence for the system is also studied.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19701018)
文摘Giorgi conjectured in 1979 that if a sequence of functionals converges in the sense of P-convergence to a limiting functional, then the corresponding gradient flows will converge as well after changing timescale appropriately. It is shown that this conjecture holds true for a rather wide kind of functionals.
文摘We obtain the H1-compactness for a system of Ginzburg-Landau equations with pinning functions and prove that the vortices of its classical solutions are attracted to the minimum points of the pinning functions. As a corollary, we construct a self-similar solution in the evolution of harmonic maps.
