Well-posedness for Cauchy fractional problems involving discrete convolution operators

2022/07/28 by González-Camus, Jorge
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2207.14110

Abstract

This work is focused on establishing sufficient conditions to guarantee the well-posedness of the following nonlinear fractional semidiscrete model \begincases \mathbb D^β_t u(n,t)= B u(n,t) + f(n-ct,u(n,t)), amp;n∈ℤ, tgt;0, u(n,0)=φ(n), amp;n∈ℤ, \endcases under the assumptions that β∈ (0,1], c>0 some constant, B is a discrete convolution operator with kernel b∈ℓ¹(\Z), which is the infinitesimal generator of the Markovian C₀-semigroup and suitable nonlinearity f. We present results concerning the existence and uniqueness of solution, as well as establishing a comparison principle of solutions according to respective initial values.

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