Abstract
Abstract
A class of integro-differential aggregation equations with nonlinear parabolic term
is considered on a compact Riemannian manifold
. The divergence term in the equations can degenerate with loss of coercivity and may contain nonlinearities of variable order. The impermeability boundary condition on the boundary
of the cylinder
is satisfied if there are no external sources of ‘mass’ conservation,
. In a cylinder
for a sufficiently small
, the mixed problem for the aggregation equation is shown to have a bounded solution. The existence of a bounded solution of the problem in the cylinder
is proved under additional conditions.
For equations of the form
with the Laplace-Beltrami operator
and an integral operator
, the mixed problem is shown to have a unique bounded solution.
Bibliography: 26 titles.
Funder
Russian Foundation for Basic Research
Subject
Algebra and Number Theory
Cited by
3 articles.
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