Energy-decreasing continuum flows of geometric order parameters are considered. The dynamics of pattern formation for an arbitrary geometric quantity is derived using a generalization of Darcy’s law based on the geometric nature of the order parameter. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanic...

In an attempt to solve Maxwell’s first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded solutions of the second order equations, which are based on the introduction of potentials, turn out to be in disagreement with a direct solution of the first...

second-order damped McKean-Vlasov stochastic evolution equations N.I. Mahmudov aand M.A. McKibben b,∗ aDepartment of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TURKEY bGoucher College, Mathematics and Computer Science Department, Baltimore, MD 21204, U S A Abstract We establish results concerning the global existence, uniqueness, approximate and exact controllab...