Stability of the Hartree equation with time-dependent coefficients
Abstract In this paper, we investigate the stability for the nonlinear Hartree equation with time-dependent coefficients i ∂ t u + Δ u + α ( t ) 1 | x | u + β ( t ) ( W ∗ | u | 2 ) u = 0 . $$i\partial_{t}u+\Delta u+ \alpha(t)\frac{1}{ \vert x \vert }u+\beta(t) \bigl(W \ast \vert u \vert ^{2}\bigr)u=...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2017-08-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-017-0854-1 |
| Summary: | Abstract In this paper, we investigate the stability for the nonlinear Hartree equation with time-dependent coefficients i ∂ t u + Δ u + α ( t ) 1 | x | u + β ( t ) ( W ∗ | u | 2 ) u = 0 . $$i\partial_{t}u+\Delta u+ \alpha(t)\frac{1}{ \vert x \vert }u+\beta(t) \bigl(W \ast \vert u \vert ^{2}\bigr)u=0. $$ We first obtain the Lipschitz continuity of the solution u = u ( α , β ) $u=u(\alpha ,\beta)$ with respect to coefficients α and β, and then prove that this equation is stable under the perturbation of coefficients. Our results improve some recent results. |
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| ISSN: | 1687-2770 |