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@ARTICLE{ncmm-2008-013,
    author = {Bul{\'{\i}}{\v c}ek, Miroslav and Consiglieri, Luisa and M{\'{a}}lek, Josef},
  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},
     month = feb,
     title = {On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures},
   journal = {Nonlinear Analysis: Real World Applications},
    volume = {12},
    number = {1},
      year = {2011},
     pages = {571--591},
      note = {NCMM Preprint no. 2008-013},
       url = {http://www.karlin.mff.cuni.cz/ncmm/preprints/08278205908MBLCJM-preprint.pdf},
       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.}
}