In particular, near singular solutions exist and singularities are prevented from occurring in finite time by mechanisms akin to those in the evolution of vortex patches.
In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations.
In other words, singular solutions always yield poor values of the objective function of ICA algorithms.
Although possessing peaked solutions in the velocity, the CH2 system does not admit singular solutions in the density profile.
An advanced and comprehensive analysis of corner singularity of linear elastostatics of different boundary conditions is established in this paper, and the singular solutions can be used in numerical computation, thus to greatly enhance the Trefftz method, including the collocation Trefftz method, the hybrid Trefftz method, the combined method, etc.
In this paper the singular solutions of linear elastostatics are derived, and two new models of interior crack singularity are proposed.
We show that the extension of the ansatz leading to singular solutions in the commutative case, yields to non self-dual (or self-antidual) configurations in noncommutative space time.
For some practical problems, the physical phenomena develop dynamically singular or nearly singular solutions in fairly localized regions, and therefore the smallest time step at each time level occurs only in these localized regions.
As consequences, we obtain (a) a doubling property for certain positive infinity-harmonic functions in smooth bounded domains and the half-space, and (b) the optimality of blowup rates of Aronsson's examples of singular solutions in cones.
A special extension of the method is devised in order to deal with singular solutions generated by point sources like monopoles or dipoles.
