Nonlocal heat equation in the Heisenberg group

RAÚL EMILIO VIDAL

NODEA. NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS (PRINTED ED.)

BIRKHAUSER VERLAG AG

Lugar: BASEL; Año: 2017

1021-9722

We study the following nonlocal diffusion equation in the Heisenberg groupu_t(z,s,t)=J*u(z,s,t)-(z,s,t),where * denote convolution product and J satisfies appropriated hypothesis. For the Cauchy problem we obtain that the asymptotic behavior of the solutions is the same form that the one for the parabolic equation for the fractional laplace operator. To obtain this result we use the spherical transform related to the pair (U(n),H_n). Finally we prove that solutions of properly rescaled nonlocal Dirichlet problem converge uniformly to the solution of the corresponding Dirichlet problem for the classical heat equation in the Heisenberg group.