This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles ...This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.展开更多
This paper is devoted to study Cauchy problems of multidimensional semilinear strictly hyperbolic equations of second order with strongly singular initial data,where the derivatives of the initial data have discontinu...This paper is devoted to study Cauchy problems of multidimensional semilinear strictly hyperbolic equations of second order with strongly singular initial data,where the derivatives of the initial data have discontinuity on two smooth curves transversally intersecting each other.The existence of the solution is proved,meanwhile,it is precisely discribed the flowery structure of the singularity of the solution.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10771024)
文摘This paper deals with propagations of singularities in solutions to a parabolic system coupled with nonlocal nonlinear sources. The estimates for the four possible blow-up rates as well as the boundary layer profiles are established. The critical exponent of the system is determined also.
文摘This paper is devoted to study Cauchy problems of multidimensional semilinear strictly hyperbolic equations of second order with strongly singular initial data,where the derivatives of the initial data have discontinuity on two smooth curves transversally intersecting each other.The existence of the solution is proved,meanwhile,it is precisely discribed the flowery structure of the singularity of the solution.
