Well posedness of general cross-diffusion systems

Global Well-Posedness of a Conservative Relaxed Cross Diffusion System

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form ui → ∂tui − ∆(ai(ũ)ui) where the ui, i = 1, ..., I represent I density-functions, ũ is a spatially regularized form of (u1, ..., uI) and the nonlinearities ai are merely assumed to be continuous and bounded from below. Existence of global weak solutions is o...

Well-posedness for General 2

We consider the Cauchy problem for a strictly hyperbolic 2 2 system of conservation laws in one space dimension u t + F (u)] x = 0; u(0; x) = u(x); (1) which is neither linearly degenerate nor genuinely non-linear. We make the following assumption on the characteristic elds. If r i (u); i = 1; 2; denotes the i-th right eigenvector of DF (u) and i (u) the corresponding eigenvalue, then the set f...

Well-posedness of Hybrid Systems

Well{posedness of Stiff Hyperbolic Systems

The theory of stii well{posedness of initial value problems for hyperbolic systems with large relaxation terms is reviewed. Furthermore, an asymptotic expansion of solutions with respect to the relaxation parameter is presented. Finally, the theory is illustrated with an example and an outlook concerning boundary value problems is given.

Perfectly Matched Layers for Hyperbolic Systems: General Formulation, Well-posedness, and Stability

Since its introduction the Perfectly Matched Layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limted to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop gen...