Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization | Zendy

Anne-Laure Dalibard | Zendy

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Kinetic Formulation for a Parabolic Conservation Law. Application to Homogenization

Author(s) -

Anne-Laure Dalibard

Publication year - 2007

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/060662770

Subject(s) - homogenization (climate) , conservation law , mathematics , kinetic energy , mathematical physics , parabolic partial differential equation , combinatorics , mathematical analysis , partial differential equation , physics , classical mechanics , biodiversity , ecology , biology

We derive a kinetic formulation for the parabolic scalar conservation law @tu + divyA(y,u) yu = 0. This allows us to define a weaker notion of solutions in L1, which is enough to recover the L1 contraction principle. We also apply this kinetic formulation to a homogenization problem studied in a previous paper; namely, we prove that the kinetic solution u" of @tu"+divxA(x/",u") " xu" = 0 behaves in L1 loc as v (x/", ¯ u(t,x)), where v is the solution of a cell problem andu the solution of the homogenized problem.

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