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I am looking for an analytic solution for the following two equations in the variables $v(x,t)$ and $u(x,t)$: $$ \begin{cases} \dfrac{\partial v}{\partial t} = -m\dfrac{\partial u}{\partial t} \\ \dfrac{\partial u}{\partial t} =-n \dfrac{\partial v}{\partial t} -av^5 \end{cases} $$ The boundary conditions are $$ v(0,t)=E\qquad u(l,t)=0 $$ The constants $m,n,a,E$ and $l$ are positive and non-zero. Thanks in advance.

Note: This is a simplified version of my earlier (unanswered) question posted on February 13, 2019.

I am looking for an analytic solution for the following two equations in the variables $v(x,t)$ and $u(x,t)$: $$ \begin{cases} \dfrac{\partial v}{\partial x} = -m\dfrac{\partial u}{\partial t} \\ \dfrac{\partial u}{\partial x} =-n \dfrac{\partial v}{\partial t} -av^5 \end{cases} $$ The boundary conditions are $$ v(0,t)=E\qquad u(l,t)=0 $$ The constants $m,n,a,E$ and $l$ are positive and non-zero. Thanks in advance.

Note: This is a simplified version of my earlier (unanswered) question posted on February 13, 2019.

I am looking for an analytic solution for the following two equations in the variables v(x,t)and u(x,t): ∂v/∂x= -m∂u/∂t and ∂u/∂x= -n∂v/∂t-av^5 The boundary conditions are v(0,t)=E and u(l,t)=0 The constants m,n,a,E and l are positive and non-zero. Thanks in advance. Note: This is a simplified version of my earlier (unanswered) question posted on February 13, 2019.

I am looking for an analytic solution for the following two equations in the variables $v(x,t)$ and $u(x,t)$: $$ \begin{cases} \dfrac{\partial v}{\partial t} = -m\dfrac{\partial u}{\partial t} \\ \dfrac{\partial u}{\partial t} =-n \dfrac{\partial v}{\partial t} -av^5 \end{cases} $$ The boundary conditions are $$ v(0,t)=E\qquad u(l,t)=0 $$ The constants $m,n,a,E$ and $l$ are positive and non-zero. Thanks in advance.

Note: This is a simplified version of my earlier (unanswered) question posted on February 13, 2019.