This paper investigates the properties of initialboundary-value problems that typically arise in technical areas. For generality, the theory of non-self-adjoint partial differential operators serves as mathematical basis. The solution of initial-boundary-value problems can be represented by means of semigroups generated by sectorial operators with compact resolvent operator. It is shown that th...

In this paper we provide‎ ‎existence results for positive solution to‎ ‎Dirichlet p(t)-Laplacian boundary value problems‎. ‎The sublinear and‎ ‎superlinear cases are considerd‎.

In this chapter we consider optimal control problems with additional inequality constraints imposed on the control unknown u and for their efficient solution we combine a primal-dual active-set strategy with the multigrid method developed in the previous chapter. Control-constraints are specified by the condition u ∈ Uad, where the set of admissible controls Uad ⊂ L(Ω) is a proper subset of L(Ω...

The concurrent FE2-method is a very powerful and flexible computational tool for multi-scale problems. However the effort high. conventional, staggered (“nested Newton”) solution scheme solves microscopic problem iteratively within each macroscopic Newton-Raphson (NR) iteration, although deformation gradients as boundary conditions at micro scale are only estimates. In this contribution monolit...

‎In this paper‎, ‎we study a class of boundary value problem‎ ‎involving the p-Laplacian oprator and singular nonlinearities‎. ‎We‎ ‎analyze the existence a critical parameter $lambda^{ast}$ such‎ ‎that the problem has least one solution for‎ ‎$lambdain(0,lambda^{ast})$ and no solution for‎ ‎$lambda>lambda^{ast}.$ We find lower bounds of critical‎ ‎parameter $lambda^{ast}$‎. ‎We use the method ...