We consider the porous medium equation with convection as follows:ut = △um+ bi. (un)xi where the summation convention is used. Assume that u = u(x,t) is a continuous weak solution of the equation in RN × (0,T] ...We consider the porous medium equation with convection as follows:ut = △um+ bi. (un)xi where the summation convention is used. Assume that u = u(x,t) is a continuous weak solution of the equation in RN × (0,T] for some T > 0 with initial condition as a Radon measure. Combining Morse iteration technique with the construction of some suitable ordinary differential equation for comparison, we have established BCP estimates for the solution u(x,t). These estimates play the main role in the studies of porous medium equation theory.展开更多
文摘We consider the porous medium equation with convection as follows:ut = △um+ bi. (un)xi where the summation convention is used. Assume that u = u(x,t) is a continuous weak solution of the equation in RN × (0,T] for some T > 0 with initial condition as a Radon measure. Combining Morse iteration technique with the construction of some suitable ordinary differential equation for comparison, we have established BCP estimates for the solution u(x,t). These estimates play the main role in the studies of porous medium equation theory.
