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 | |
| Added by: | [JH] |
| Total mark: | 0 |
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