The parabolic integro-differential equation under investigation, $$ {\beta}\partial_t u = Au - m * Au + {\chi}\tag1 $$(1) subject to suitable initial and boundary conditions (BC), represents linear, non-homogeneous diffusion with memory kernel $m = m[t]$, in the space-time domain $Q$.
Crosta, G. (2010). Mathematical Review of MR2558302 "A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination." by Janno, Jaan; Kasemets, Kairi. MATHEMATICAL REVIEWS.
Mathematical Review of MR2558302 "A positivity principle for parabolic integro-differential equations and inverse problems with final overdetermination." by Janno, Jaan; Kasemets, Kairi
CROSTA, GIOVANNI FRANCO FILIPPO
2010
Abstract
The parabolic integro-differential equation under investigation, $$ {\beta}\partial_t u = Au - m * Au + {\chi}\tag1 $$(1) subject to suitable initial and boundary conditions (BC), represents linear, non-homogeneous diffusion with memory kernel $m = m[t]$, in the space-time domain $Q$.
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