Semilinear subdiffusion with memory in multidimensional domains

Mykola Krasnoschok, Vittorino Pata and Nataliya Vasylyeva

Mathematische Nachrichten, 2019, vol. 292, issue 7, 1490-1513

Abstract: For ν∈(0,1), we investigate the nonlinear integro‐differential equation on a multidimensional space domain Ω⊂RnDtνu−L1u−∫0tK(t−s)L2u(·,s)ds=f(x,t,u)+g(x,t)where Dtν is the Caputo fractional derivative and L1 and L2 are uniform elliptic operators with smooth coefficients depending on time. Under suitable conditions on the nonlinearity, the global existence and uniqueness of the classical solution to the related initial and boundary value problems are established.

Date: 2019
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