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A note on the spatial approximation of PDEs with unbounded coefficients : The special one-dimensional case

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Resumo:We consider the spatial approximation of the Cauchy problem for a linear uniformly parabolic PDE of second order, with nondivergent operator and unbounded time- and space-dependent coefficients, where equation’s free term and initial data are also allowed to grow. We concentrate on the special case where the PDE has one dimension in space. As in [10], we consider a suitable variational framework and approximate the PDE problem’s generalised solution in the spatial variable, with the use of finite-difference methods, but we obtain, for this case, consistency and convergence results sharper than the corresponding results obtained in [10] for the more general multidimensional case.
Autores principais:Gonçalves, F.F.
Outros Autores:Grossinho, Maria do Rosário; Morais, E.
Assunto:Cauchy Problem Parabolic PDEs Unbounded Coefficients Non-divergent Operators Weighted Sobolev Spaces Finite-difference Methods
Ano:2020
País:Portugal
Tipo de documento:artigo
Tipo de acesso:acesso aberto
Instituição associada:Universidade de Lisboa
Idioma:inglês
Origem:Repositório da Universidade de Lisboa

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