We consider here the Cauchy problem for the full system of dynamic Von KK armm an equations, which is a model for the vibrations of a nonlinear elastic plate. We prove global existence and uniqueness of nite energy solutions in the case of an innnite plate. We show then that our methods and results still hold for a rectangular plate which is simply supported or clamped at the boundary. Moreover...

In this paper we study an integro-differential equation that arises in modeling slow erosion of granular flow. We construct piecewise constant approximate solutions, using a front tracing technique. Convergence of the approximate solutions is established through proper a priori estimates, which in turn gives global existence of BV solutions. Furthermore, continuous dependence on initial data an...

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization ...

‎Independent random‎ ‎variables $Y_{1},ldots‎ ,‎Y_{n}$ belongs to the‎ ‎proportional reversed hazard rate (PRHR) model with‎ ‎proportionality parameters $lambda_1,...,lambda_n$‎, ‎if‎ ‎$Y_{k}sim G^{lambda _{k}}(x)$‎, ‎for $k=1,...,n$‎, ‎where $G$ is an‎ ‎absolutely continuous distribution function‎. ‎In this paper we compare‎ ‎the smallest order‎ ‎statistics‎, ‎the sample ranges and th...

Let X=(X1 ,X2 ) be a continuous random vector. Under the assumption that the marginal distributions of X1 and X2 are given, we develop models for vector X when there is partial information about the dependence structure between X1  and X2. The models which are obtained based on well-known Principle of Maximum Entropy are called the maximum entropy (ME) mo...

Abstract In this paper, we give some basic concepts of q -calculus that will be needed in paper. Then, built the q-nonlocal condition ensures solution existence and uniqueness fractional q-integrodifferential equation. Also, introduce continuous dependence solution. We find numerical using finite-difference-Trapezoidal cubic B-spline-Trapezoidal methods. Finally, three examples to illustrate va...

We show that Hölder continuous incompressible Euler flows satisfy the local energy inequality (“globally dissipative” solutions) exhibit nonuniqueness and contain examples strictly dissipate kinetic energy. The collection of such solutions emanating from a fixed initial data may have positive Hausdorff dimension in space even if equality is imposed, set giving rise to an infinite family $$C^0$$...