Wellposedness and regularity of a variable-order space-time fractional diffusion equation
Xiangcheng Zheng, Hong Wang
Abstract
We prove wellposedness of a variable-order linear space-time fractional diffusion equation in multiple space dimensions. In addition we prove that the regularity of its solutions depends on the behavior of the variable order (and its derivatives) at time [Formula: see text], in addition to the usual smoothness assumptions. More precisely, we prove that its solutions have full regularity like its integer-order analogue if the variable order has an integer limit at [Formula: see text] or have certain singularity at [Formula: see text] like its constant-order fractional analogue if the variable order has a non-integer value at time [Formula: see text].
Topics & Concepts
MathematicsInteger (computer science)Variable (mathematics)Order (exchange)SmoothnessConstant (computer programming)Space (punctuation)DiffusionMathematical analysisFractional calculusSingularityDiffusion equationPhysicsMetric (unit)ThermodynamicsOperations managementFinanceEconomicsPhilosophyLinguisticsComputer scienceProgramming languageFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods