Joel E. Restrepo

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math.AP2024

Evolutionary integro-differential equations of scalar type on locally compact groups

Santiago Gómez Cobos, Joel E. Restrepo, Michael Ruzhansky

We study existence, uniqueness, norm estimates and asymptotic time behaviour (in some cases can be claimed to be sharp) for the solution of a general evolutionary integral (differe…

math.AP2024

$L^{p} - L^{q}$ estimates for non-local heat and wave type equations on locally compact groups

Santiago Gómez Cobos, Joel E. Restrepo, Michael Ruzhansky

We prove the $L^{p} - L^{q}$ $(1 < p ⩽ 2 ⩽ q < + \infty)$ norm estimates for the solutions of heat and wave type equations on a locally compact separable unimodular group $G$ by…

math.AP2023

Heat and wave type equations with non-local operators, II. Hilbert spaces and graded Lie groups

Marianna Chatzakou, Joel E. Restrepo, Michael Ruzhansky

We study heat and wave type equations on a separable Hilbert space $H$ by considering non-local operators in time with any positive densely defined linear operator with d…

Evolutionary integro-differential equations of scalar type on locally compact groups

Lp−Lq estimates for non-local heat and wave type equations on locally compact groups

Heat and wave type equations with non-local operators, II. Hilbert spaces and graded Lie groups

$L^{p} - L^{q}$ estimates for non-local heat and wave type equations on locally compact groups