Geodesic
Initial boundary value problem for Sobolev type nonlinear equations
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2006), pp. 33-40 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper following initial boundary value problem is considered. $$\left\{\begin{array}{l} A\left(\frac{\partial u}{\partial t}\right)+Bu=f,\\ u(0)=u_0,\\ D^{\gamma}u\Big|_{\Gamma}=0, |\gamma|\leq m, \end{array}\right.$$ Operators A and B are nonlinear and have the following forms $Au=\displaystyle\sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^{\alpha}A_{\alpha}(x,t,D^{\gamma}u),\quad Bu=\displaystyle\sum_{|\alpha|\leq m}(-1)^{|\alpha|}D^{\alpha}B_{\alpha}(x,t,D^{\gamma}u),~~|\gamma|\leq m.$ Conditions for functions $A_{\alpha}(x,t,\xi_{\gamma})$ and $B_{\alpha}(x,t,\xi_{\gamma})$ are obtained that lead to existence and uniqueness of solution of the problem in the spaces $L^p(0,T,W^m_p),~р\geq 2$. 
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     author = {H. A. Mamikonyan},
     title = {Initial boundary value problem for {Sobolev} type nonlinear equations},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {33--40},
     year = {2006},
     number = {2},
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     url = {http://geodesic.mathdoc.fr/item/UZERU_2006_2_a2/}
}
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H. A. Mamikonyan. Initial boundary value problem for Sobolev type nonlinear equations. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2006), pp. 33-40. http://geodesic.mathdoc.fr/item/UZERU_2006_2_a2/

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