# Reference request for a particular type of evolutionary problems

I am currently interested in the system of equations of the form, $$$$\begin{cases} \dfrac{du}{dt} + Au\ni f(u)\\[0.2cm] u(0)=u_0 \end{cases}$$$$

where the operator $$A:D(A)\subset X\to X^*$$ is nonlinear, $$X$$ is a Banach space and the functional $$f=f(u)$$ is linear.

I know some of the wellposedness results for the nonhomogeneous problems where the RHS term $$f=f(t)$$. I am also aware of some results for the evolution equations (as above) for semilinear equations where $$A$$ is linear and $$f=f(u)$$ is nonlinear. Can somebody point out some references / articles / books which discusses the type of evolution equation which I mentioned. Thanks in advance.

You can check the following recent paper and the references therein

COMPACT ALMOST AUTOMORPHIC WEAK SOLUTIONS FOR SOME MONOTONE DIFFERENTIAL INCLUSIONS: APPLICATIONS TO PARABOLIC AND HYPERBOLIC EQUATIONS, B. Es-sebbar et al. (2019).

• Thank you. I will have a look. – Hirak Dec 31 '19 at 9:53