Time-fractional equations with reaction terms: fundamental solutions and asymptotics

2019/03/28 by Dipierro, Serena, Pellacci, Benedetta, Valdinoci, Enrico +1 · 3 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.11939

Abstract

We analyze the fundamental solution of a time-fractional problem, establishing existence and uniqueness in an appropriate functional space. We also focus on the one-dimensional spatial setting in the case in which the time-fractional exponent is equal to, or larger than, \frac12. In this situation, we prove that the speed of invasion of the fundamental solution is at least `almost of square root type', namely it is larger than~ct^β for any given~c>0 and~β∈(0,\frac12).

Cited by

• A parametrix construction for time-fractional partial differential equations
• Blow-Up Results of Time Fractional Heat Equation With Nonlinear Neumann Boundary Conditions
• Asymptotic behavior of the fundamental solution of space-time fractional equations with a reaction term

Related

• Asymptotic behavior of the fundamental solution of space-time fractional equations with a reaction term
• Asymptotic behaviors of fundamental solution and its derivatives related to space-time fractional differential equations
• Critical parameters for reaction-diffusion equations involving\n space-time fractional derivatives
• Computational solutions of unified fractional reaction-diffusion equations with composite fractional time derivative
• Time Fractional Poisson Equations: Representations and Estimates