Existence of solutions for an inhomogeneous fractional semilinear heat equation

Solvability of Superlinear Fractional Parabolic Equations

“…The literature is now very extensive and we refer to the comprehensive monograph [35]. We also mention the following works, some of which are directly related to this paper, others with a different emphasis (higher order equations, systems, nonlinear boundary conditions): superlinear parabolic equations [2, 6, 7, 14, 29-31, 33, 36, 38-41]; linear heat equation with nonlinear boundary conditions [10,15,20,27,28] ; superlinear parabolic equations with a potential [1,3,9,22,23,39]; superlinear parabolic systems [11-13, 26, 34]; superlinear fractional parabolic equations [18,19,21,32,37]; superlinear higher order parabolic equations [8,16,17,24,25].…”

“…Of course, by translation invariance the singularity could be located at any point of R N . Subsequently, the results of [19] were extended to some related parabolic problems with a power law nonlinearity (see [20][21][22][23][24][25]). However, one cannot apply the arguments in these papers to problem (P) with a general nonlinearity F since they depend heavily upon the homogeneous structure of the power law nonlinearity.…”

Cauchy problem for a fractional anisotropic parabolic equation in anisotropic Hölder spaces

“…Some other questions of regularity and qualitative behavior of solutions to fractional equations of the kind were considered, in particular, in [2], [46], [3], [10], [22], [25], [39].…”