Well posed Cauchy problems for complex nonlinear equations must be semilinear.
Well posedness under Levi conditions for a degenerate second order Cauchy problem
Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations
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 of the Dirichlet problem and homotopy classification of elliptic systems of second-order partial differential equations