TY  - JOUR
ID  - ncmm-2008-013
T1  - On solvability of a non-linear heat equation with a non-integrable convective term and data involving measures
A1  - Bulíček, Miroslav
A1  - Consiglieri, Luisa
A1  - Málek, Josef
JA  - Nonlinear Analysis: Real World Applications
Y1  - 2011
VL  - 12
IS  - 1
SP  - 571
EP  - 591
N1  - NCMM Preprint no. 2008-013
UR  - http://www.karlin.mff.cuni.cz/ncmm/preprints/08278205908MBLCJM-preprint.pdf
M2  - doi: 10.1016/j.nonrwa.2010.07.001
KW  - Almost everywhere convergence of gradients
KW  - Convective term
KW  - Entropy solution
KW  - existence
KW  - large data
KW  - Lipschitz approximation of a Bochner function
KW  - Non-linear convection–diffusion equation
KW  - Non-linear heat equation
KW  - weak solution
N2  - 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.
ER  -