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Some non-standard sobolev spaces, interpolation and its application to PDE
González Nogueras, María del Mar; Gualdani, Maria
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic equations where the nonlinearity is highly degenerate and depends on the smoothness of the solution at a certain subset (that may vary with time). An example of application is a diffusion equation with a smooth free boundary, and a moving source/sink where the solution has singularity. The main new idea here is to characterize the functional space setting that is needed for semigroup theory to apply.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Functional spaces
Nonlinear parabolic equation
Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems
Classificació AMS::35 Partial differential equations::35S Pseudodifferential operators and other generalizations of partial differential operators
Classificació AMS::26 Real functions::26A Functions of one variable
Classificació AMS::46 Associative rings and algebras::46B Normed linear spaces and Banach spaces; Banach lattices
Attribution-NonCommercial-NoDerivs 3.0 Spain

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