Heat Equation with Memory in Anisotropic and Non-Homogeneous Media
Abbreviated Journal Title
Acta. Math. Sin.-English Ser.
Heat equation with memory; anisotropic and non-homogeneous media; well-posedness; propagation speed; FINITE PROPAGATION SPEED; INTEGRODIFFERENTIAL EQUATIONS; EVOLUTION-EQUATIONS; WAVE-PROPAGATION; LA CHALEUR; CONDUCTION; DERIVATIVES; LEQUATION; THEOREM; Mathematics, Applied; Mathematics
A modified Fourier's law in an anisotropic and non-homogeneous media results in a heat equation with memory, for which the memory kernel is matrix-valued and spatially dependent. Different conditions on the memory kernel lead to the equation being either a parabolic type or a hyperbolic type. Well-posedness of such a heat equation is established under some general and reasonable conditions. It is shown that the propagation speed for heat pulses could be either infinite or finite, depending on the different types of the memory kernels. Our analysis indicates that, in the framework of linear theory, heat equation with hyperbolic kernel is a more realistic model for the heat conduction, which might be of some interest in physics.
Acta Mathematica Sinica-English Series
"Heat Equation with Memory in Anisotropic and Non-Homogeneous Media" (2011). Faculty Bibliography 2010s. 2151.