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On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures
Type of publication: Article
Citation: ncmm-2008-013
Publication status: Published
Journal: Nonlinear Analysis: Real World Applications
Volume: 12
Number: 1
Year: 2011
Month: February
Pages: 571--591
Note: NCMM Preprint no. 2008-013
URL: http://www.karlin.mff.cuni.cz/...
DOI: 10.1016/j.nonrwa.2010.07.001
Abstract: Considering a mixed boundary-value problem for a non-linear heat equation with the non-homogeneous Neumann condition, the right-hand side and the initial condition in space of sign-measures, we establish large-data existence results even if the convective term is not integrable. In order to develop a theory under minimal assumptions on given data, we deal with two concepts of solution: weak solution (for data in measures) and entropy solution (for L1-data). Regarding the entropy solution we identify conditions ensuring its uniqueness. Improved properties of the Lipschitz approximations of Bochner functions represent an important tool in establishing the existence of large-data solutions.
Keywords: Almost everywhere convergence of gradients, Convective term, Entropy solution, existence, large data, Lipschitz approximation of a Bochner function, Non-linear convection–diffusion equation, Non-linear heat equation, weak solution
Authors Bulíček, Miroslav
Consiglieri, Luisa
Málek, Josef
Added by: [JH]
Total mark: 0
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