A nonlinear nonlocal multi-dimensional conservation law

[摘要] We study a continuous model which describes the mass transport in droplet dispersions. The model is formulated as a conservation law with several space-variables, partial derivative n/partial derivative t + partial derivative(Gn)/partial derivative r + Sigma(j=1)(m) partial derivative(H(j)n)/partial derivative x(j) = 0, for t > 0, r > 0, x(j) > 0, and Sigma(j = 1)(m) x(j) = 1, where G, H-j (j = 1,..., m) are nonlocal functions of the unknown n(t,r,x(1),...,x(m)); moreover, they have exponential singularities at r = 0. We prove global existence and uniqueness and establish some numerical properties of the solution. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-01