Convex semigroups on $$L^p$$-like spaces

Abstract In this paper, we investigate convex semigroups on Banach lattices with order continuous norm, having $$L^p$$ Lp -spaces in mind as a typical application. We show that the basic results from linear $$C_0$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">C0 -semigroup theory extend to case. prove generator of is closed and uniquely determines semigroup whenever domain dense. Moreover, invariant under semigroup, result leads well-posedness related Cauchy problem. last step, provide conditions for existence strong continuity envelopes families -semigroups. The are discussed several examples such semilinear heat equations nonlinear integro-differential equations.