Existence and uniqueness of solutions for an abstract nonlinear hyperbolic-parabolic equation

Abstract

We study a wide class of abstract nonlinear evolution equation of the type (l) A₂u″+A₁uprime;+Au+M(u)=f(t) in a Hilbert space H where A₁ A₂ are bounded symmetric linear operators, A is a positive definite self-adjoint operator, M is a monotone operator and f is a given function. We include the possibility of A₂≥0. We prove the existence and uniqueness of global weak solutions for equation (l) and illustrate our results with several examples of this family of hyperbolic-parabolic equations in mathematical physics.

AMS (MOS):

• 35L15