Time-Dependent Problems

In this chapter, we will apply the general theory developed in the preceding sections to evolution problems of the following general form: Find u ∈ V satisfying (9.1) ( ∂ t u,ψ)+a(u)(ψ)=f ∀ψ∈W, t∈(0,T], u(0)=u(0)= u 0 <![CDATA[$$({\partial _t}u,\psi ) + a(u)(\psi ) = f{\text{ }}\forall \psi \in W,\q... View More