Well-posedness for a nonlocal nonlinear diffusion equation and applications to inverse problems

ABSTRACT

This article investigates a space–time fractional diffusion equation with a nonlinear source and a space nonlocal operator. The well-posedness is demonstrated from using contraction mapping theorem and generalized Gronwall's inequality firstly. Based on the forward problem, we prove that a nonlinear source term and a fractional order of time derivative are uniquely determined by data which can be observed at one fixed spatial point.

COMMUNICATED BY:

• Dinghua Xu

Keywords:

• Determination of fractional order
• inverse source problem
• unique existence
• nonlocal nonlinear diffusion equation

2010 Mathematics Subject Classifications:

• 35R11
• 35R30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [Grants Nos 11871392, 11771347, 91730306, 41390454].