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Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²

Agnieszka Herczak, Michał Olech (2009)

Banach Center Publications

We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.

Existence and continuous dependence results in the dynamical theory of piezoelectricity

Michele Ciarletta (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The paper is concerned with the dynamical theory of linear piezoelectricity. First, an existence theorem is derived. Then, the continuous dependence of the solutions upon the initial data and body forces is investigated.

Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.

Lucie Baudouin (2005)

Revista Matemática Complutense

We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and...

Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems

Irena Pawłow, Antoni Żochowski (2003)

Banach Center Publications

A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.

Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains

Rodolfo Salvi (2005)

Banach Center Publications

In the paper [13], we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in [13] to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence...

Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions

Le Thi Phuong Ngoc, Nguyen Thanh Long (2016)

Applications of Mathematics

In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...

Currently displaying 921 – 940 of 3659