It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are es...It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values.展开更多
In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliar...In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliary function and other methods,we prove the local existence of solutions,and under appropriate conditions the blowup time and blowup rate estimation are given.Finally,numerical experiments are given to illustrate the blowup behavior of the solution.展开更多
We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here ...We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here κ > 0 does not depend on the initial data.This is achieved by proving the regularity of solutions under■ This new scaling invariance also motivates us to construct an explicit type-Ⅱ blowup solution for γ > 1.展开更多
文摘It is dealt with positive solutions to the systems: u-t-u- XX =v+p, v-t-v XX =u+q in Ω×(0, T) subject to either initial conditions or boundary_value conditions. The exact blowup rate estimates of solution are established under some monotonicity assumptions on the initial values.
文摘In this article,we discuss the blowup phenomenon of solutions to the wdiffusion equation with Dirichlet boundary conditions on the graph.Through Banach fixed point theorem,comparison principle,construction of auxiliary function and other methods,we prove the local existence of solutions,and under appropriate conditions the blowup time and blowup rate estimation are given.Finally,numerical experiments are given to illustrate the blowup behavior of the solution.
基金supported by National Natural Science Foundation of China (Grant No. 11725102)National Support Program for Young Top-Notch Talents+3 种基金SGST 09DZ2272900 from Shanghai Key Laboratory for Contemporary Applied Mathematicssupported by Zheng Ge Ru Foundation, Hong Kong RGC Earmarked Research Grants (Grant Nos. CUHK-14305315, CUHK-14300917 and CUHK-14302917)NSFC/RGC Joint Research Scheme Grant (Grant No. N-CUHK 443-14)a Focus Area Grant from the Chinese University of Hong Kong
文摘We find a new scaling invariance of the barotropic compressible Navier-Stokes equations. Then it is shown that type-Ⅰ singularities of solutions with■ can never happen at time T for all adiabatic number γ 1. Here κ > 0 does not depend on the initial data.This is achieved by proving the regularity of solutions under■ This new scaling invariance also motivates us to construct an explicit type-Ⅱ blowup solution for γ > 1.
