We study the decay/growth rates in all Lp norms of solutions to an inhomogeneousnonlocal heat equation in RN involving a Caputo -time derivative and a power of the Laplacianwhen the dimension is large, N > 4. Rates depend ...

A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction ...

We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary ...

We characterize the weighted Lebesgue spaces, Lp(ℝn, v(x)dx), for which the solutions of the Heat and Poisson problems have limits a.e. when the time t tends to zero. © 2012 American Mathematical Society.

We study the large-time behavior in all Lp norms and in different space-time scales of solutions to a nonlocal heat equation in ℝN involving a Caputo α-time derivative and a power of the Laplacian (−Δ)s, s ∈ (0,1), extending ...

We deal with anomalous diffusions induced by continuous time random walks - CTRW in ℝn. A particle moves in ℝn in such a way that the probability density function u(·, t) of finding it in region Ω of ℝn is given by ∫Ωu(x, ...

We study the large-time behavior in all Lp norms of solutions to a heat equation with a Caputo α-time derivative posed in RN (0 < α < 1). These are known as subdiffusion equations. The initial data are assumed to be ...

A non-classical one dimensional Stefan problem with thermal coefficients temperature dependent and a Robin type condition at fixed face x=0 for a semi-infinite material is considered. The source function depends on the ...

We prove space-time parabolic Besov regularity in terms of integrability of Besov norms in the space variable for solutions of the heat equation on cylindrical regions based on Lipschitz domains.