$L^{p}$-$L^{q}$ time decay estimates for the solution of the linear partial differential equations of thermodiffusion
Volume 37 / 2010
Applicationes Mathematicae 37 (2010), 143-170
MSC: 35G16, 35G25, 35G55, 35M13.
DOI: 10.4064/am37-2-2
Abstract
We consider the initial-value problem for a linear hyperbolic parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove $L^p$-$L^q$ time decay estimates for the solution of the associated linear Cauchy problem.
