A class of integro-differential aggregation equations with nonlinear parabolic term ##IMG## [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn1.gif] {$b(x,u)_t$} is considered on a compact Riemannian manifold ##IMG## [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn2.gif] {$\mathscr{M}$} . 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 ##IMG## [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn3.gif] {$\partial\mathscr{M}\times[0,T]$} of the cylinder ##IMG## [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn4.gif] {$Q^T=\mathscr{M}\times[0,T]$} is satisfied if there are no external sources of ‘mass’ conservation, ##IMG## [http:...] {$\displaystyle\int_\mathscr{M}b(x,u(x,t))\,d\nu=\mathrm{const}$}

中文翻译：

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黎曼流形上积分-微分聚合方程弱解的存在性和唯一性

一类具有非线性抛物线项## IMG ##的积分微分聚合方程[http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn1.gif] {$ b（x， u）_t $}放在紧凑的黎曼流形上## IMG ## [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn2.gif] {$ \ mathscr {M } $}。方程中的发散项会随着矫顽力的损失而退化，并且可能包含可变阶数的非线性。边界## IMG ##上的不可渗透边界条件[http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn3.gif] {$ \ partial \ mathscr {M} \ times圆柱体## IMG ##的[0，T] $} [http://ej.iop.org/images/1064-5616/211/2/226/MSB_211_2_226ieqn4.gif] {$ Q ^ T = \ mathscr如果没有“质量”守恒的外部来源，则满足{M} \ times [0，T] $}，## IMG ## [http：...] {$ \ displaystyle \ int_ \ mathscr {M} b （X，