The quenching of solutions to time-space fractional Kawarada problems

Abstract

Quenching solutions to a Kawarada problem with a Caputo time-fractional derivative and a fractional Laplacian are considered. The solutions to such problems may only exist locally in time when quenching occurs. Quenching and non-quenching solutions are shown to remain positive and be monotonically increasing in time under minor restrictions. Conditions for quenching to occur are demonstrated and shown to depend on the domain size.

arXiv comment21 pages, article has already been accepted (uploading to complete arXiv profile)

References in corpus (3)

• Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach
• On the positivity, monotonicity, and stability of a semi-adaptive LOD method for solving three-dimensional degenerate Kawarada equations
• On a Nonuniform Crank-Nicolson Scheme for Solving the Stochastic Kawarada Equation via Arbitrary Grids

Cited by in corpus (4)

• Fast implicit difference schemes for time-space fractional diffusion equations with the integral fractional Laplacian
• A positivity- and monotonicity-preserving nonlinear operator splitting approach for approximating solutions to quenching-combustion semilinear partial differential equations
• A series representation of the discrete fractional Laplace operator of arbitrary order
• Object classification in analytical chemistry via data-driven discovery of partial differential equations