Singular Right-hand Sides Research Articles

The equicontinuity condition for sequences of solution spaces

The verification of an appropriately stated equicontinuity condition for a sequence of solution spaces is one of the two key points in the theory of the Cauchy problem for equations with singular right-hand sides. We obtain a related sufficient condition.

Application of an analog of the δc-model to the analysis of strength of elastoplastic cracked shellsto the analysis of strength of elastoplastic cracked shells

We propose a method for the investigation of the limiting equilibrium of elastoplastic shells with systems of interacting cracks. It can be described as follows: By using an analog of the δc-model, the elastoplastic problem is reduced to an elastic problem of the limiting equilibrium of a shell with cracks of unknown length whose lips are subjected to the action of unknown forces and moments satisfying the conditions of plasticity for thin shells. By using equations of the general moment theory of shells and the theory of generalized functions, we reduce the problem to the solution of a system of singular integral equations with unknown limits of integration and singular right-hand sides. We construct an algorithm for the numerical solution of systems of this sort supplemented by the conditions of boundedness of stresses and conditions of plasticity. We investigate crack tip opening displacements in a closed cylindrical shell with a regular system of longitudinal cracks or two transverse cracks. For a cylindrical shell with a single crack, we present an approximate relation for the determination of the critical load or crack length.

On a singular differential system arising from a min-max control problem

The feedback law for a control problem with a nondifferentiable cost functional is characterized by an initial-value problem for a differential system with singular right-hand side. This system is characteristic for a partial differential equation formally satisfied by the feedback law. A regularization of the differential system and the partial differential equation is given, and the feedback laws for the smoothed problems are shown to converge to the original feedback law.

On a general method for integrating Schrödinger's equation with singular right-hand side in a constant homogeneous electromagnetic field

On a general method for integrating Schrödinger's equation with singular right-hand side in a constant homogeneous electromagnetic field