2次元の偏微分方程式の解き方

以下の各初期値を用いて、式1より"u(x,y)"を解きたいのですが、MATLABで解く方法がわかりません。もし詳しい方いらっしゃいましたら教えていただきたいです。

%初期値
alpha=0.03;
beta=4;
nx=8;
ny=8;
ita=0.03;
u=zeros(nx,ny);
e=zeros(nx,ny);
m_0=[0 0 0 0.5 0.5 0.1 0.7 0.4; %m_0は各要素が[0,1]を満たす、nx × nyのランダムな行列   
    0.2 0.2 0.2 0 0 0 0 0;
    0.1 0 0 0 0.3 0.5 0.9 0;
    0.3 0.1 0.2 0 0 0.5 0 0;
    0 0 0 0.5 0.5 0.1 0.7 0.4;
    0.2 0.2 0.2 0 0 0 0 0;
    0.1 0 0 0 0.3 0.5 0.9 0;
    0.3 0.1 0.2 0 0 0.5 0 0];


%以下の式を解きたい
alpha*laplacian(u,[x y])=beta*u-(m_0)   %式1

[Dyuman Joshi]

You want to take laplacian of a zeros array?

Or is u a function?

[Honoka Kobayashi]

u that I want to solve with equation 1 is a function, not a zeros array at the end .

"u=zeros(nx,ny)" is just initial state.

I'd like to know u(x, y) when I solve equation 1.

[Dyuman Joshi]

"u that I want to solve with equation 1 is a function"

Then please provide the definition of u.

[Honoka Kobayashi]

u is not clear function, but it's a function that is derived by equation 1.