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IJMMS
ASYMPTOTICS FOR CRITICAL NONCONVECTIVE TYPE EQUATIONS
NAKAO HAYASHI
**ELENA** **I**. **KAIKINA**
PAVEL I. NAUMKIN
We study large-time asymptotic behavior of solutions to the Cauchy problem for a model of ... 1.1 is proved.
Acknowledgments. The work of **Elena** **I**. **Kaikina** and Pavel I. Naumkin is partially
supported by CONACYT. The authors are grateful to the unknown referees for many
useful suggestions and

IJMMS
ASYMPTOTICS FOR CRITICAL NONCONVECTIVE TYPE EQUATIONS
NAKAO HAYASHI
**ELENA** **I**. **KAIKINA**
PAVEL I. NAUMKIN
We study large-time asymptotic behavior of solutions to the Cauchy problem for a model of ... 1.1 is proved.
Acknowledgments. The work of **Elena** **I**. **Kaikina** and Pavel I. Naumkin is partially
supported by CONACYT. The authors are grateful to the unknown referees for many
useful suggestions and

?ticas, UNAM Campus Morelia , AP 61-3 Xangari, 58089 Morelia, MICH , Mexico
Correspondence should be addressed to **Elena** **I**. **Kaikina**; We study the equations governing the high-speed transmission in long

?ticas, UNAM Campus Morelia , AP 61-3 Xangari, 58089 Morelia, MICH , Mexico
Correspondence should be addressed to **Elena** **I**. **Kaikina**; We study the equations governing the high-speed transmission in long

**Elena** **I**. **Kaikina**. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the

? Lp,a < ? .
k
**Elena** **I**. **Kaikina** 3
where ? > 0 is sufficiently small. We assume that the nonlinear term N(u, ux) is of critical
convective type from the point of view of the large-time asymptotic ... asymptotic formulas (4.2)), therefore by the Cauchy theorem
and symmetrical properties of function H, we can change the contour of integration ? to
the imaginary axis (?i?, i?) to get
**Elena** **I**. **Kaikina** 11
(3.16

We study nonlinear nonlocal equations on a half-line in the critical case $$ \left\{ {\begin{array}{l} {\partial _{{t\,}} u + \,\beta |u|^{\alpha } \,u\, + \,\mathbb{K}u = 0,\,\,\,\,x\, > \,0,\,\,t > \,0,\,} \\ {u(0,x)\, = \,u_{0} \,(x)\,,\,\,\,\,x\, > \,0,} \\ {\partial _{x}^{{j - 1\,}} \,u\,(0,t)\, = \,0,\,j\, = \,1,\,\ldots,\,M} \\ \end{array} } \right. $$ where \(\beta \in...