Abstract theorems of existence, uniqueness and regularity of the solution are proved for a differential equation whose solution takes its values in a sequence of Banach spaces called a Banach scale. The abstract theorems are then applied to obtain existence, uniqueness and regul…
Recent techniques in partial differential equations have led to a solution to the general multidimensional Cauchy problem for nonlinear gradient waves. In a blown-up configuration, Sablé-Tougeron constructs a local solution for a quasilinear hyperbolic system with continuous Cau…
In multidimension, the Cauchy problem for a first order quadrilinear strictly hyperbolic system with a continuous data whose first derivatives are discontinuous on an hypersurface, is a free characteristic boundaries problem. We solve it locally in a blown-up configuration into …
We consider a system of n conservation laws: [partial derivative/boundary/degree of a polynomial symbol]∂u [over] [partial derivative/boundary/degree of a polynomial symbol]∂t + [partial derivative/boundary/degree of a polynomial symbol]∂f(u) [over] [partial derivative/boundary/…