Well-posedness and asynchronous exponential growth of solutions of a two-phase cell division model.
Well-posedness and ill-posedness of the fifth-order modified KdV equation.
Well-posedness and regularity for a parabolic-hyperbolic Penrose-Fife phase field system
This work is concerned with the study of an initial boundary value problem for a non-conserved phase field system arising from the Penrose-Fife approach to the kinetics of phase transitions. The system couples a nonlinear parabolic equation for the absolute temperature with a nonlinear hyperbolic equation for the phase variable , which is characterized by the presence of an inertial term multiplied by a small positive coefficient . This feature is the main consequence of supposing that the response...
Well-posedness and regularity of hyperbolic boundary control systems on a one-dimensional spatial domain
We study a class of hyperbolic partial differential equations on a one dimensional spatial domain with control and observation at the boundary. Using the idea of feedback we show these systems are well-posed in the sense of Weiss and Salamon if and only if the state operator generates a C0-semigroup. Furthermore, we show that the corresponding transfer function is regular, i.e., has a limit for s going to infinity.
Well-posedness and regularity results for a dynamic von Kármán plate.
Well-posedness and scattering for the KP-II equation in a critical space
Wellposedness and stability results for the Navier-Stokes equations in
Well-posedness for a class of non-Newtonian fluids with general growth conditions
The paper concerns uniqueness of weak solutions to non-Newtonian fluids with nonstandard growth conditions for the Cauchy stress tensor. We recall the results on existence of weak solutions and additionally provide the proof of existence of measure-valued solutions. Motivated by the fluids of strongly inhomogeneous behaviour and having the property of rapid shear thickening we observe that the described situation cannot be captured by power-law-type rheology. We describe the growth conditions with...
Well-posedness for density-dependent incompressible fluids with non-Lipschitz velocity
This paper is dedicated to the study of the initial value problem for density dependent incompressible viscous fluids in with . We address the question of well-posedness for large and small initial data having critical Besov regularity in functional spaces as close as possible to the ones imposed in the incompressible Navier Stokes system by Cannone, Meyer and Planchon (where with ). This improves the classical analysis where is considered belonging in such that the velocity remains...
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
Well-posedness for some perturbations of the KdV equation with low regularity data.
Well-posedness for systems representing electromagnetic/acoustic wavefront interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Well-posedness for Systems Representing Electromagnetic/Acoustic Wavefront Interaction
In this paper we consider dispersive electromagnetic systems in dielectric materials in the presence of acoustic wavefronts. A theory for existence, uniqueness, and continuous dependence on data is presented for a general class of systems which include acoustic pressure-dependent Debye polarization models for dielectric materials.
Wellposedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid
In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space , or . The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary...
Well-posedness in the Gevrey classes of the Cauchy problem for a non-strictly hyperbolic equation with coefficients depending on time
Well-posedness issues for the Prandtl boundary layer equations
These notes are an introduction to the recent paper [7], about the well-posedness of the Prandtl equation. The difficulties and main ideas of the paper are described on a simpler linearized model.
Well-posedness of a Cauchy problem involving nonlinear fractal dissipative equations.
Well-posedness of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain
In this paper, we study a class of Initial-Boundary Value Problems proposed by Colin and Ghidaglia for the Korteweg-de Vries equation posed on a bounded domain (0,L). We show that this class of Initial-Boundary Value Problems is locally well-posed in the classical Sobolev space Hs(0,L) for s > -3/4, which provides a positive answer to one of the open questions of Colin and Ghidaglia [Adv. Differ. Equ. 6 (2001) 1463–1492].
Well-Posedness of a Semilinear Heat Equation with Weak Initial Data.
Well-posedness of a thermo-mechanical model for shape memory alloys under tension
We present a model of the full thermo-mechanical evolution of a shape memory body undergoing a uniaxial tensile stress. The well-posedness of the related quasi-static thermo-inelastic problem is addressed by means of hysteresis operators techniques. As a by-product, details on a time-discretization of the problem are provided.