A singular operator with Cauchy kernel on the subspaces of weight Lebesgue space is considered. A sufficient condition for a bounded action of this operator from a subspace to another subspace of weight Lebesgue space of functions is found. These conditions are not identical withMuckenhoupt conditions. Moreover, the completeness, minimality, and basicity of sines and cosines systems are conside...

The space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigate...

We explore numerically the evolution of a collapsing spherical shell of charged, massless scalar field. We obtain an external ReissnerNördstrom space-time, and an inner space-time that is bounded by a singularity on the Cauchy Horizon. We compare these results with previous analysis and discuss some of the numerical problems encountered.

In this paper, we shall define and study the concept of  -statistical convergence and  -statistical Cauchy in random 2-normed space. We also introduce the concept of  -statistical completeness which would provide a more general frame work to study the completeness in random 2-normed space. Furthermore, we also prove some new results.

Consider a strictly hyperbolic nn system of conservation laws in one space dimension: u t + F(u) x = 0: () Relying on the existence of the Standard Riemann Semigroup generated by (), we establish the uniqueness of entropy-admissible weak solutions to the Cauchy problem, under a mild assumption on the variation of u along space-like segments.

We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter whose coefficients depend holomorphically on ( , t) near the origin in C and are bounded holomorphic on some horizontal strip in C w.r.t the space variable. In our previous contribution [14], we assumed the forcing term of the Cauchy problem to be analytic near 0. Presently, we consider a family of...

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a ...

The relative power of actions in a Cauchy body suffering mutations due to defect evolution is introduced. It is shown that its invariance under the action of the Euclidean group over the ambient space and the material space allows one to obtain (i) the balance of standard and configurational actions and (ii) the identification of configurational ingredients from a unique source.

We consider the Schrödinger equation with derivative perturbation terms in one space dimension. For the linear equation, we show that the standard Strichartz estimates hold under specific smallness requirements on the potential. As an application, we establish existence of local solutions for quadratic derivative Schrödinger equations in one space dimension with small and rough Cauchy data.