Mathematical Models in Electrical Circuits

I. Dissipative operators and differential equations on Banach spaces.- 1.0. Introduction.- 1.1. Duality type functionals.- 1.2. Dissipative operators.- 1.3. Semigroups of linear operators.- 1.4. Linear differential equations on Banach spaces.- 1.5. Nonlinear differential equations on Banach spaces.- II. Lumped parameter approach of nonlinear networks with transistors.- 2.0. Introduction.- 2.1. Mathematical model.- 2.2. Dissipativity.- 2.3. DC equations.- 2.4. Dynamic behaviour.- 2.5. An example.- III. lp-solutions of countable infinite systems of equations and applications to electrical circuits.- 3.0. Introduction.- 3.1. Statement of the problem and preliminary results.- 3.2. Properties of continuous lp-solutions.- 3.3. Existence of continuous lp-solutions for the quasiautonomous case.- 3.4. Truncation errors in linear case.- 3.5. Applications to infinite circuits.- IV. Mixed-type circuits with distributed and lumped parameters as correct models for integrated structures.- 4.0. Why mixed-type circuits?.- 4.1. Examples.- 4.2. Statement of the problem.- 4.3. Existence and uniqueness for dynamic system.- 4.4. The steady state problem.- 4.5. Other qualitative results.- 4.6. Bibliographical comments.- V. Asymptotic behaviour of mixed-type circuits. Delay time predicting.- 5.0. Introduction.- 5.1. Remarks on delay time evaluation.- 5.2. Asymptotic stability. Upper bound of delay time.- 5.3. A nonlinear mixed-type circuit.- 5.4. Comments.- VI. Numerical approximation of mixed models for digital integrated circuits.- 6.0. Introduction.- 6.1. The mathematical model.- 6.2. Construction of the system of FEM-equations.- 6.2.1. Space discretization of reg-lines.- 6.2.2. FEM-equations of lines.- 6.3. FEM-equations of the model.- 6.4. Residual evaluations.- 6.5. Steady state.- 6.6. The delay time and its a-priori upper bound.- 6.7. Examples.- 6.8. Concluding remarks.- Appendix I.- List of symbols.- References.