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A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.
Grzegorz Karch, and Kanako Suzuki. "Blow-up versus global existence of solutions to aggregation equations." Applicationes Mathematicae 38.3 (2011): 243-258. <http://eudml.org/doc/279888>.
@article{GrzegorzKarch2011, abstract = {A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.}, author = {Grzegorz Karch, Kanako Suzuki}, journal = {Applicationes Mathematicae}, keywords = {nonlocal parabolic equation; moment method; nonlocal and nonlinear transport term; convolution}, language = {eng}, number = {3}, pages = {243-258}, title = {Blow-up versus global existence of solutions to aggregation equations}, url = {http://eudml.org/doc/279888}, volume = {38}, year = {2011}, }
TY - JOUR AU - Grzegorz Karch AU - Kanako Suzuki TI - Blow-up versus global existence of solutions to aggregation equations JO - Applicationes Mathematicae PY - 2011 VL - 38 IS - 3 SP - 243 EP - 258 AB - A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions. LA - eng KW - nonlocal parabolic equation; moment method; nonlocal and nonlinear transport term; convolution UR - http://eudml.org/doc/279888 ER -