Yes, the eigenfunction (with boundary condition $u(0,t)=0$) are in the form of $sin(m_1\pi x/L) sin (m_2\pi y/L)$, with $m_1=0,1,2,...$ and $m_2 = 0,1,2,...$. In this case $\lambda = m_1^2 + m_2^2$.
↧
