Long time dynamics of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects

We consider a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects which is introduced in [2]. It comprised equation to describe tumor growth, coupled reaction-diffusion type for generic nutrient the tumor. An additional couples concentration prostate-specific antigen (PSA) prostatic tissue it obeys linear equation. The system completes homogeneous Dirichlet boundary conditions variable Neumann condition PSA. Here we investigate long time dynamics model. We first prove that initial-boundary value problem generates strongly continuous semigroup on suitable phase space admits global attractor proper space. Moreover, also discuss convergence solution single stationary state obtain rate estimate under some coefficients.