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

Author

Listed:
  • Yabing Gao

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

  • Yongxiang Li

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

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.

Suggested Citation

  • Yabing Gao & Yongxiang Li, 2020. "Initial Boundary Value Problems of Semi-Linear Sub-Diffusion with Gradient Terms," Mathematics, MDPI, vol. 8(10), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1665-:d:420465
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