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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…