Existence of weak solutions for abstract hyperbolic-parabolic equations - Marcondes Rodrigues Clark (International Journal of Mathematics and Mathematical Sciences)
In this paper we study the Existence and Uniqueness of solutions for the following Cauchy problem:A2u″(t)+A1u′(t)+A(t)u(t)+M(u(t))=f(t),   t∈(0,T)       (1)u(0)=u0;   A2u′(0)=A212u1;                      where A1 and A2 are bounded linear operators in a Hilbert space H, {A(t)}0≤t≤T is a family of self-adjoint operators, M is a non-linear map on H and f is a function from (0,T) with values in H.