@article{Li2023, 
author = {Yaning Li and Yuting Yang},
title = {Blow-up and global existence of solutions for time-space fractional pseudo-parabolic equation},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {8},
pages = {17827-17859},
keywords = {fractional pseudo-parabolic equation, blow-up, global existence, Cauchy problems},
url = {https://www.sciopen.com/article/10.3934/math.2023909},
doi = {10.3934/math.2023909},
abstract = {In this article, we consider the Cauchy problem for the following time-space fractional pseudo-parabolic equations         {                                                                              0                                      C                                            D                          t                                      α                                (          I          −          m          Δ          )          u          +                                    (                              −                Δ                            )                                                      β                2                                              u          =                      |                    u                                    |                                      p              −              1                                u          ,                    x          ∈                                    R                                      N                                ,                    t          >          0          ,                                      u          (          0          ,          x          )          =                      u                          0                                (          x          )          ,                                                                                          x          ∈                                    R                                      N                                ,                        where    0  <  α  <  1  ,    0  <  β  <  2  ,    p  >  1  ,    m  >  0  ,        u          0        ∈      L          q            (                  R                    N              )  . An estimating        L    p    −      L    q   for solution operator of time-space fractional pseudo-parabolic equations is obtained. The critical exponents of this problem are determined when        u    0    ∈      L          q        (            R              N        )  . Moreover, we also obtain global existence of the mild solution when        u    0    ∈      L    p    (            R              N        )  ∩      L    q    (            R              N        ) small enough.}
}