This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...

This paper considers the global classical solvability (well-posedness) of a mixed initial-boundary value problem for semilinear hyperbolic systems with nonlinear reaction coupling of Lotka–Volterra type. The reaction nonlinearity is not globally Lipschitz in L2 and has Lipschitz properties depending on an L∞-norm bound. The well-posedness problem is reformulated in an abstract setting as a modi...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

In this paper a special complex Kn of abstract cubes [2, 3], which contains only n-dimensional cubes is examined. The border of this complex is an abstract (n − 1)-dimensional sphere. It is proved that the abstract sphere contains at least one 0dimensional cube, which belongs to exactly n cubes with dimension 1, if the complex is a homogeneous n-dimensional tree. This result allows to solve, in...

In isotropic finite elasticity, unlike in the linear elastic theory, a homogeneous Cauchy stress may be induced by non-homogeneous strains. To illustrate this, we identify compatible nonhomogeneous three-dimensional deformations producing a homogeneous Cauchy stress on a cuboid geometry, and provide an example of an isotropic hyperelastic material, which is not rank-one convex, and for which th...

In this paper, we discuss a new generalization of univariate skew-Cauchy distribution with two parameters, we denoted this by GSC(&lambda1, &lambda2), that it has more flexible than the skew-Cauchy distribution (denoted by SC(&lambda)), introduced by Behboodian et al. (2006). Furthermore, we establish some useful properties of this distribution and by two numerical example, show that GSC(&lambd...

In this paper we propose a computational method for solving a Cauchy problem of Laplace’s equation. By using the Green formula, the Cauchy problem is transformed to a moment problem so that numerical computations by using a regularization technique can be achieved. Stability estimation and suitable choice of regularization parameter for the proposed method are also given. For numerical verifica...

Introduction Partial differential equations on bounded domains of R n have traditionally been equipped with homogeneous boundary conditions (usually Dirichlet, Neumann, or Robin). However, other kinds of boundary conditions can also be considered, and for a number of concrete application it seems that dynamic (i.e., time-dependent) boundary conditions are the right ones. Motivated by physical p...

We consider the inverse problem to recover a part Γc of the boundary of a simply connected planar domain D from a pair of Cauchy data of a harmonic function u in D on the remaining part ∂D \ Γc when u satisfies a homogeneous impedance boundary condition on Γc. Our approach extends a method that has been suggested by Kress and Rundell [17] for recovering the interior boundary curve of a doubly c...