Benjamin-Ono equation on a half-line.
Blow-up results for some reaction-diffusion equations with time delay
We discuss the effect of time delay on blow-up of solutions to initial-boundary value problems for nonlinear reaction-diffusion equations. Firstly, two examples are given, which indicate that the delay can both induce and prevent the blow-up of solutions. Then we show that adding a new term with delay may not change the blow-up character of solutions.
Boundedness in a fully parabolic chemotaxis system with signal-dependent sensitivity and logistic term
Boundedness of solutions to parabolic-elliptic chemotaxis-growth systems with signal-dependent sensitivity
This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function and the growth term under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that