6533b7d0fe1ef96bd125a484

RESEARCH PRODUCT

Renormalized solutions for degenerate elliptic–parabolic problems with nonlinear dynamical boundary conditions and L1-data

José M. MazónJulián ToledoNoureddine IgbidaFuensanta Andreu

subject

Renormalized solutionsApplied MathematicsDegenerate energy levelsMathematical analysisMixed boundary conditionHele–Shaw problemWeak formulationMultiphase Stefan problemsNonlinear systemNeumann boundary conditionFree boundary problemUniquenessBoundary value problemAnalysisMathematicsDegenerate elliptic–parabolic problems

description

Abstract We consider a degenerate elliptic–parabolic problem with nonlinear dynamical boundary conditions. Assuming L 1 -data, we prove existence and uniqueness in the framework of renormalized solutions. Particular instances of this problem appear in various phenomena with changes of phase like multiphase Stefan problems and in the weak formulation of the mathematical model of the so-called Hele–Shaw problem. Also, the problem with non-homogeneous Neumann boundary condition is included.

yearjournalcountryeditionlanguage
2008-06-01Journal of Differential Equations
10.1016/j.jde.2008.02.022http://dx.doi.org/10.1016/j.jde.2008.02.022