3 papers
math.AP2026
Fractional very fast diffusion equations in Lebesgue spaces: uniqueness and smoothing effects
Mohammed-El-Mahdi Boudaoud, Arturo de Pablo, Fernando Quirós
We investigate forward and backward smoothing effects in Lebesgue spaces and for the Cauchy problem associated to the nonlinear and nonlocal fra…
math.AP2024
Blow-up for a double nonlocal heat equation
Raúl Ferreira, Arturo de Pablo
We study the blow-up question for the diffusion equation involving a nonlocal derivative in time defined by convolution with a nonnegative and nonincreasing kernel, and a nonlocal…
math.AP2024
Positivity and asymptotic behaviour of solutions to a generalized nonlocal fast diffusion equation
Arturo de Pablo, Fernando Quirós, Jorge Ruiz-Cases
We study the positivity and asymptotic behaviour of nonnegative solutions of a general nonlocal fast diffusion equation, \[\partial_t u + \mathcal{L}φ(u) = 0,\] and the interplay b…