Fractional diffusion-wave equations with critical nonlinearities in Lebesgue spaces

TL;DR

This paper investigates semilinear fractional diffusion-wave equations with critical nonlinearities, establishing local well-posedness, spatial regularity, continuous dependence, and global solutions with asymptotic analysis.

Contribution

It provides new results on existence, regularity, and long-term behavior of solutions for fractional diffusion-wave equations with critical nonlinearities.

Findings

Proved local well-posedness and regularity of solutions.

Established existence of global mild solutions.

Analyzed asymptotic behavior of solutions.

Abstract

This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the continuous dependence of the solutions on initial data. Secondly, we establish the existence of global mild solutions and investigate their asymptotic behavior.