Weak solutions to initial-boundary-value problems for quasilinear evolution equations of an odd order

Initial-boundary-value problems in three diffierent domains are considered for quasilinear evolution partial differential equations of an odd (not less than third) order with respect to spatial variables in the multidimensional case. The nonlinearity has the divergent form and at most a quadratic rate of growth. Assumptions on the differential operator of odd order provide global estimates on solutions in L2 and a local smoothing effect. Results on existence and uniqueness of global weak solutions are established. The essential part of the study is the construction of special solutions to the corresponding linear equations of the "boundary potential" type, which ensures the results under natural smoothness assumptions on initial and boundary data provided we have certain relations between the dimension and the order of the equations.

Authors
Editors
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Publisher
-
Number of issue
5-6
Language
English
Pages
421-470
Status
Published
Department
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DOI
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Number
-
Volume
17
Year
2012
Organizations
  • 1 Peoples' Friendship University of Russia, Miklukho-Maklai str. 6, Moscow, 117198, Russian Federation
Keywords
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Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2213/