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A mathematical erythrocyte model based on weak solutions of integral equations

“…Let the permittivity ε in (x) be a Hölder continuous function inD in ; then each solution of the volume integro-differential equation (8) representable in D in and D e as the sum of a differentiable field and the gradient of a continuously differentiable function is a classical solution of the original differential problem (6), (7). Conversely, the electric field E of an arbitrary classical solution of problem (6), (7) is a solution of the volume integro-differential equation (8).…”

“…By transferring the differentiation operators into the integrand in (8) and by using the theorem on the differentiation of an integral with a weak singularity [11], we obtain the vector singular integral equation [12] E(x) + 1 3…”

“…Let us proceed to the construction of an approximate solution following the general scheme of the discrete source method [8]. Since the particle surface is axisymmetric, we pass from the problem of approximating the fields on the surface (2) to the successive solution of the transmission problems on the generator in of the surface of revolution ∂D in for the Fourier harmonics of fields with respect to the azimuthal variable.…”

“…By analogy with [8], we construct an approximate solution that takes into account not only the axial symmetry of the scatterer but also the polarization of the incident plane wave. Consider the case of the P -polarization.…”

“…Since the scheme of the numerical algorithm of the discrete source method remains the same as in [8], we indicate only the main differences.…”