Abstract
The one-dimensional porous media equation u t = ( u m ) x x {u_t} = {({u^m})_{xx}} , m > 1 m > 1 , is considered for x ∈ R x \in R , t > 0 t > 0 with initial conditions u ( x , 0 ) = u 0 ( x ) u(x,0) = {u_0}(x) integrable, nonnegative and with compact support. We study the behaviour of the solutions as t → ∞ t \to \infty proving that the expressions for the density, pressure, local velocity and interfaces converge to those of a model solution. In particular the first term in the asymptotic development of the free-boundary is obtained.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
