Initial Boundary Value Problems of Semi-Linear Sub-Diffusion with Gradient Terms

Yabing Gao and Yongxiang Li
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Yabing Gao: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
Yongxiang Li: Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2020, vol. 8, issue 10, 1-14

Abstract: We consider the existence and uniqueness of the saturated classical solutions and the positive classical solutions to initial boundary value problems of semi-linear sub-diffusion with gradient terms. Applying this to the fractional power of the sectorial operator theory and the imbedding theory in the interpolation spaces, where the nonlinear term satisfies more general conditions, we obtain the existence and uniqueness of the saturated classical solutions. The results obtained generalize the recent conclusions on this topic. Finally, an example is given to illustrate the feasibility of our main results.

Keywords: fractional partial differential equations; gradient terms; classical solutions; fractional power of sectorial operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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