Evolution equations and subdifferentials in Banach spaces (Q1422473)

The authors investigate the Cauchy problem \[ \frac{du}{dt}(t)+\partial \varphi^1(u(t))-\partial \varphi^2(u(t))\ni f(t),\quad 0<t<T\text{ in }V^*,\qquad u(0)=u_0,\tag{CP} \] where \(V^*\) is the dual space of a real reflexive Banach space \(V\). Under suitable assumptions on \(\varphi^1\) and \(\varphi^2\) it is proved the existence of the strong solutions of (CP). Applications to an initial-boundary value problem for the nonlinear heat equation are also presented.