Multispecies Lotka–Volterra competition–diffusion system with forcing terms depending on the variables

In this paper, we study the diffusive Lotka–Volterra system containing the variable coefficients. In the Sobolev‐space settings, we achieve the well‐posedness properties (existence and regularity) and large‐time asymptotics (continuation and global existence or finite‐time blowup) of the solutions in the Sobolev spaces and time‐weighted Sobolev spaces.