Mathematical Study of the Nonlinear Singular Integral Magnetic Field Equation. II

Source abstract

For the numerical treatment of the nonlinear singular integral magnetic field equation $R{\bf M} = h{\bf M} + A{\bf M} = {\bf H}_a$, which has been considered by the author in Part I [SIAM J. Appl. Math., 39 (1980), pp. 14-20]. Tucker stability is established in the case where $(h{\bf M})(x) = {\bf g}({\bf M}(x),x)$ is a bounded, continuous, and strongly monotone operator in ${\bf L}^2$. In the special cases ${\bf g}({\bf M},x) = c{\bf M}$ and ${\bf g}({\bf M},x) = g(M,x){{\bf M}/M}$, which are important for engineering applications, explicit perturbation estimates are obtained.