This volume is a collection of research papers on nonlinear partial differential equations and related areas, representing many aspects of the most recent developments in these important areas. In particular, the following are included: nonlinear conservation laws, semilinear elliptic equations, nonlinear hyperbolic equations, nonlinear parabolic equations, singular limit problems, and analysis of exact and numerical solutions. Important areas such as numerical analysis, relaxation theory, multiphase theory, kinetic theory, combustion theory, dynamical systems, and quantum field theory are also covered.
Relaxation limits for a class of balance laws and kinetic formulation; large-time behaviour of entropy solutions in L for multidimensional scalar conservation laws; indefinite elliptic problems with critical exponents; nonlinear diffusive-dispersive limits for multidimensional conservation laws; plainleve analysis and its application; the stability of travelling wave solutions for a rate-type viscoelastic system;generalized rankine-Hugoniot relations of delta-shocks in solutions of transportation equations; a note on development of singularities of solutions of nonlinear hyperbolic partial differential equations; strange attractors in pseudospectral solutions of the dissipative Zakharov equations; string-like defects and fractional total curvature in a gauged harmonic map model; on half-space problems for the heat equations with nonlinear boundary conditions; systems of conservation laws with incomplete sets of eigenvectors everywhere. (Part contents).