6533b827fe1ef96bd1286447
RESEARCH PRODUCT
Porous medium equation with absorption and a nonlinear boundary condition
José M. MazónFuensanta AndreuJulio D. RossiJulián Toledosubject
Applied MathematicsMathematical analysisNeumann boundary conditionFree boundary problemNo-slip conditionBoundary (topology)UniquenessBoundary value problemAnalysisRobin boundary conditionPoincaré–Steklov operatorMathematicsdescription
where is a bounded domain with smooth boundary, @=@ is the outer normal derivative, m ? 1; p; and q are positive parameters and u0 is in L∞( ). Problems of this form arise in mathematical models in a number of areas of science, for instance, in models for gas or :uid :ow in porous media [3] and for the spread of certain biological populations [13]. In the semilinear case (that is for m=1), there is an extensive literature about global existence and blow-up results for this type of problems, see among others, [5,9,16] and the literature therein. For the degenerate case (that is for m = 1), with a nonlinear boundary condition, local existence and uniqueness of weak solutions which are limit of solutions of nondegenerate problems has been established in [1]. Also in [2] existence and uniqueness of global weak solutions for a similar
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-05-01 | Nonlinear Analysis: Theory, Methods & Applications |