Global Well posedness for Fractional Sobolev Galpern Type Equations
This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the sou...
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oai:http:--repository.vlu.edu.vn-:123456789-10722022-11-09T15:01:06Z Global Well posedness for Fractional Sobolev Galpern Type Equations Huy Tuan Nguyen Nguyen Anh Tuan Chao Yang "fractional pseudo-parabolic globally Lipschitz source exponential nonlinearity global well-posedness." This article is a comparative study on an initial-boundary value problem for a class of semilinear pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree of the source nonlinearity on the well-posedness of the solution. By considering four different types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding to the four cases of the nonlinear source terms. For the advection source function case, we apply a nontrivial limit technique for singular integral and some appropriate choices of weighted Banach space to prove the global existence result. For the gradient nonlinearity as a local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming the smallness of the initial data we derive the global well-posed results. And for the case of exponential nonlinearity in two-dimensional space, we derive the global well-posedness by additionally use of Orlicz space. 2022-11-09T08:01:06Z 2022-11-09T08:01:06Z 2021 Resource Types::text::journal::journal article http://repository.vlu.edu.vn:443/handle/123456789/1072 10.48550/arXiv.2108.07681 en_US Discrete & Continuous Dynamical Systems 1553-5231 text/plain |
| institution |
Trường Đại học Văn Lang |
| collection |
DSpaceVLU |
| language |
en_US |
| topic |
"fractional pseudo-parabolic globally Lipschitz source exponential nonlinearity global well-posedness." |
| spellingShingle |
"fractional pseudo-parabolic globally Lipschitz source exponential nonlinearity global well-posedness." Huy Tuan Nguyen Nguyen Anh Tuan Chao Yang Global Well posedness for Fractional Sobolev Galpern Type Equations |
| description |
This article is a comparative study on an initial-boundary value problem for a class of semilinear
pseudo-parabolic equations with the fractional Caputo derivative, also called the fractional
Sobolev-Galpern type equations. The purpose of this work is to reveal the influence of the degree
of the source nonlinearity on the well-posedness of the solution. By considering four different
types of nonlinearities, we derive the global well-posedness of mild solutions to the problem corresponding
to the four cases of the nonlinear source terms. For the advection source function
case, we apply a nontrivial limit technique for singular integral and some appropriate choices of
weighted Banach space to prove the global existence result. For the gradient nonlinearity as a
local Lipschitzian, we use the Cauchy sequence technique to show that the solution either exists
globally in time or blows up at finite time. For the polynomial form nonlinearity, by assuming
the smallness of the initial data we derive the global well-posed results. And for the case of exponential
nonlinearity in two-dimensional space, we derive the global well-posedness by additionally
use of Orlicz space. |
| format |
Resource Types::text::journal::journal article |
| author |
Huy Tuan Nguyen Nguyen Anh Tuan Chao Yang |
| author_facet |
Huy Tuan Nguyen Nguyen Anh Tuan Chao Yang |
| author_sort |
Huy Tuan Nguyen |
| title |
Global Well posedness for Fractional Sobolev Galpern Type Equations |
| title_short |
Global Well posedness for Fractional Sobolev Galpern Type Equations |
| title_full |
Global Well posedness for Fractional Sobolev Galpern Type Equations |
| title_fullStr |
Global Well posedness for Fractional Sobolev Galpern Type Equations |
| title_full_unstemmed |
Global Well posedness for Fractional Sobolev Galpern Type Equations |
| title_sort |
global well posedness for fractional sobolev galpern type equations |
| publishDate |
2022 |
| url |
http://repository.vlu.edu.vn:443/handle/123456789/1072 |
| work_keys_str_mv |
AT huytuannguyen globalwellposednessforfractionalsobolevgalperntypeequations AT nguyenanhtuan globalwellposednessforfractionalsobolevgalperntypeequations AT chaoyang globalwellposednessforfractionalsobolevgalperntypeequations |
| _version_ |
1792767595096571904 |