Abstract: We introduce some fuzzy set-valued functional equations, i.e. the generalized Cauchy type (in n variables), the Quadratic type, the Quadratic-Jensen type, the Cubic type and the Cubic-Jensen type fuzzy set-valued functional equations and discuss the Hyers-Ulam-Rassias stability of the above said functional equations. These results can be regarded as an important extension of stability...

This article is devoted to the analysis of a two-space dimensional linear parabolic equation, subject to Cauchy-Dirichlet boundary conditions. The problem is set in a conical type domain and the right hand side term of the equation is taken in a Lebesgue space. One of the main issues of this work is that the domain can possibly be non regular. This work is an extension of the symmetric case stu...

In this paper, we provide uniform estimates for V-cycle algorithms with one smoothing on each level. This theory is based on some elliptic regularity but does not require a smoother interaction hypothesis (sometimes referred to as a strengthened Cauchy Schwarz inequality) assumed in other theories. Thus, it is a natural extension of the full regularity V-cycle estimates provided by Braess and H...

n this paper, we apply picard’s iteration method followed by adomian decomposition method to solve a nonlinear singular cauchy problem of euler- poisson- darboux equation. the solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by carroll and showalter (1976)in the solution of singular cauchy problem.

This paper is devoted to studying a two-component peakon system with cubic nonlinearity, which extension of the Camassa–Holm equation. We first discuss local well-posedness for Cauchy problem system. Then, in light fine structure system, we present precise blow-up scenario strong solutions and derive new result respect initial data. Finally, are discussed as well.

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

Cauchy-compact flat spacetimes with extreme BTZ are Lorentzian analogue of complete hyperbolic surfaces finite volume. Indeed, the latter 2-manifolds locally modeled on plane, group isometries $\mathrm{PSL}_2(\R)$, admitting finitely many cuspidal ends while regular part former 3-manifolds models 3 dimensionnal Minkowski space, $\mathrm{PSL}_2(\R)\ltimes \RR^3$, whose neighborhoods foliated by ...

The new global version of the Cauchy-Kovalevskaia theorem presented here is a strengthening and extension of the regularity of similar global solutions obtained earlier by the author. Recently the spacetime foam differential algebras of generalized functions with dense singularities were introduced. A main motivation for these algebras comes from the so called space-time foam structures in Gene...