We discuss a new solution algorithm for quasi-static elastoplastic problems with hardening. Such problems are described by a time dependent variational inequality, where the displacement and the plastic strain fields serve as primal variables. After discretization in time, one variational inequality of the second kind is obtained per time step and can be reformulated as each one minimization pr...

The undamped wave equation on an open domain of arbitrary dimension and boundary of class C 1 is considered. On parts of the boundary the normal derivative of the solution equals the convolution of its time derivative with a measure of positive type. This setting subsumes standard disssipative boundary conditions as well as the interaction with vis-coelastic boundary materials. Applying methods...

This study develops a hybrid ensemble-variational approach for solving data assimilation problems. The method, called TR-4D-EnKF, is based on a trust region framework and consists of three computational steps. First an ensemble of model runs is propagated forward in time and snapshots of the state are stored. Next, a sequence of basis vectors is built and a lowdimensional representation of the ...

We study calculus of variations problems, where the Lagrange function depends on the Caputo-Katugampola fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives, with dependence on a real parameter ρ. We present sufficient and necessary conditions of first and second order to determine the extremizers of a functiona...

In this paper we investigate existence of solutions for the system: Dtαu=div(u∇p),Dtαp=−(−Δ)sp+u2,in T3 0<s≤1, and 0<α≤1. The term Dtαu denotes Caputo derivative, which models memory effects in time. fractional Laplacian (−Δ)s represents Lévy diffusion. We prove global nonnegative weak that satisfy a variational inequality. proof uses several approximations steps, including an implicit Euler ti...

We consider the Schrödinger equation with a nonlinear derivative term on [0, +∞) under Robin boundary condition at 0. Using virial argument, we obtain existence of blowing up solutions, and using variational techniques, stability instability by blow-up results for standing waves.

This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized ?-Caputo fractional derivative with weight. Depending on critical point theorems some properties ?-Caputo-type integration differentiation, variational construction multiplicity result solutions are established.

The fractal derivative is adopted to describe the non-linear fractional wave equation in a space. A variational principle successfully established by semi-inverse method. two-scale method and He?s exp-function are used solve equation, good result obtained.

In this paper, we consider the partial differential equations approach for valuing European and American style options on multiple assets. We use a method of lines finite element implementation available in the software package FEMLAB in order to solve the variational inequality that characterizes the American style option, as well as the partial differential equation that defines the European ...

&lt;abstract&gt;&lt;p&gt;The aim of this work is to study several problems the calculus variations, where dynamics state function given by a generalized fractional derivative. This derivative combines two well-known concepts: with respect another and variable order. We present Euler–Lagrange equation, which necessary condition that every optimal solution problem must satisfy. Other are also stu...