Regularity properties and blow-up of the solutions for improved Boussinesq equations
In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence, uniqueness, and regularity properties of the solu...
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2021
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Boussinesq egyenlet, Differenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2021.1.89 |
| Online Access: | http://acta.bibl.u-szeged.hu/75810 |
| LEADER | 02170nas a2200241 i 4500 | ||
|---|---|---|---|
| 001 | acta75810 | ||
| 005 | 20220523131506.0 | ||
| 008 | 220523s2021 hu o 0|| eng d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2021.1.89 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a eng | ||
| 100 | 1 | |a Shakhmurov Veli | |
| 245 | 1 | 0 | |a Regularity properties and blow-up of the solutions for improved Boussinesq equations |h [elektronikus dokumentum] / |c Shakhmurov Veli |
| 260 | |c 2021 | ||
| 300 | |a 21 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a In this paper, we study the Cauchy problem for linear and nonlinear Boussinesq type equations that include the general differential operators. First, by virtue of the Fourier multipliers, embedding theorems in Sobolev and Besov spaces, the existence, uniqueness, and regularity properties of the solution of the Cauchy problem for the corresponding linear equation are established. Here, L p -estimates for a solution with respect to space variables are obtained uniformly in time depending on the given data functions. Then, the estimates for the solution of linearized equation and perturbation of operators can be used to obtain the existence, uniqueness, regularity properties, and blow-up of solution at the finite time of the Cauchy for nonlinear for same classes of Boussinesq equations. Here, the existence, uniqueness, L p -regularity, and blow-up properties of the solution of the Cauchy problem for Boussinesq equations with differential operators coefficients are handled associated with the growth nature of symbols of these differential operators and their interrelationships. We can obtain the existence, uniqueness, and qualitative properties of different classes of improved Boussinesq equations by choosing the given differential operators, which occur in a wide variety of physical systems. | |
| 650 | 4 | |a Természettudományok | |
| 650 | 4 | |a Matematika | |
| 695 | |a Boussinesq egyenlet, Differenciálegyenlet | ||
| 700 | 0 | 1 | |a Shahmurov Rishad |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/75810/1/ejqtde_2021_089.pdf |z Dokumentum-elérés |