Abstract
We study nonlinear pseudodifferential equations on a half-line with a nonanalytic symbol \begin{equation*} \left\{ \begin{array}{c} \partial _{t}u+\mathbb{K}u=\lambda \left\vert u\right\vert ^{\sigma }u,\text{ }x\in \mathbf{R}^{+},\text{ }t>0, \\ u\left( 0,x\right) =u_{0}\left( x\right) \text{, }x\in \mathbf{R}^{+}, \end{array} \right. \end{equation*} where $0<$ $\sigma <1,$ $\lambda \in \mathbf{R}$ and \begin{equation*} \mathbb{K}u=\frac{1}{2\pi i}\theta (x)\int_{-i\infty }^{i\infty }e^{px}K(p) \widehat{u}(t,p)dp,\qquad K(p)=\frac{p^{2}}{p^{2}-1}. \end{equation*} The aim of this paper is to prove the global existence of solutions to the initial-boundary-value problem and to find the main term of the asymptotic representation of solutions in subcritical case, when the nonlinear term of equation has the time decay rate less than that of the linear terms.
Citation
Elena I. Kaikina. "Subcritical pseudodifferential equation on a half-line with nonanalytic symbol." Differential Integral Equations 18 (12) 1341 - 1370, 2005. https://doi.org/10.57262/die/1356059714
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