Blow-Up of Solutions to Fractional-in-Space Burgers-Type Equations

Abstract

We consider fractional-in-space analogues of Burgers equation and Korteweg-de Vries-Burgers equation on bounded domains. Namely, we establish sufficient conditions for finite-time blow-up of solutions to the mentioned equations. The obtained conditions depend on the initial value and the boundary conditions. Some examples are provided to illustrate our obtained results. In the proofs of our main results, we make use of the test function method and some integral inequalities.

Keywords

• fractional-in-space Burgers equation
• fractional-in-space Korteweg-de Vries-Burgers equation
• global solution
• blow-up