The authors of this article study the existence and uniqueness of weak solutions of the initial-boundary value problem for u t = div((|u| σ + d 0)|▽u|p(x,t)-2▽u)+f(x,t)(0<σ<2).They apply the method of parabolic regularization and Galerkin's method to prove the existence of solutions to the mentioned problem and then prove the uniqueness of the weak solution by arguing by contradiction.The authors prove that the solution approaches 0 in L 2(Ω) norm as t →∞.
In this paper,a system of reaction-diffusion equations arising in a nutrient-phytoplankton populations is investigated.The equations model a situation in which phytoplankton population is divided into two groups,namely susceptible phytoplankton and infected phytoplankton.A number of existence and non-existence results about the non-constant steady states of a reaction diffusion system are given.If the diffusion coefficient of the infected phytoplankton is treated as bifurcation parameter,non-constant positive steady-state solutions may bifurcate from the constant steady-state solution under some conditions.
In this paper,a class of one-dimension p-Laplacian equation with nonlocal initial value is studied.The existence of solutions for such a problem is obtained by using the topological degree method.
