Cauchy problems and applications (Q1590115)

The author studies the Cauchy problem \[ {du\over dt}\in Au,\;t>0,\;u(0)=u_0, \] for \(u:[0,\infty)\to X\), where \(X\) is a real Banach space and \(A\) is a nonlinear multi-valued operator in \(X\) satisfying accretiveness and range conditions. Using the method of lines, the author shows that the problem has a limit solution. Under the hypothesis that \(A\) is `embeddedly demi-closed', it is shown that the limit solution is a strong solution. Further results are given for linear \(A\). The result is applied to nonlinear partial differential equations.