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Diffusion-aggregation processes with mono-stable reaction terms
Existence and uniqueness of nonlinear impulsive integro-differential equations
| 1. | Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore-641 004, India |
| 2. | Department of Mathematics, PSG of Arts and Sciences, Coimbatore, India |
$u'(t)= Au(t)+f(t,u(t),\int_0^tk(t,s)u(s)ds),
t>0, t\ne t_i,$
$u(0)= u_0,$
$\Delta u(t_i)=
I_i(u(t_i)). i= 1,2,....,p.$
in a Banach space X, where A is the infinitesimal generator of a strongly continuous semigroup,$ \Delta u(t_i)=u(t^+_i)-u(t^-_i)$ and $I's$ are some operator. We apply the semigroup theory to study the existence and uniqueness of the mild solutions, and then show that the mild solution give rise to classical solution if $f$ is continuously differentiable.
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