Applying porous medium equation on images

I wanted to apply the 2D porous medium equation on images. I am using the finite difference scheme for PDEs (FTCS method). The code works for m=1 (Standard Diffusion Equation), but not working for higher values of m. I get a black image as an output. Can someone tell me where I am going wrong ? Here is the code:

% To apply the porous medium equation u_t=laplacian(u^m) on images
% 
% We shall use the finite difference approximation scheme for the
% derivatives

% Accept Image and stop time from the user
disp('Enter Image');
im=uigetfile('*.jpg','Select the Image file');
gm=input('Enter gamma value: ');
T1=input('Enter stop time: ');

% input image file and store in u1
u1=double(imread(im));

% Display Original Image
subplot(1,2,1), imshow(uint8(u1))
title('Original image');

% store size in m and n
[m,n,~]=size(u1);

% step size along t
dt=0.1;

for t = 0:dt:T1

   % finite difference approximation for u_x
   u_x = (u1(:,[2:n n],:) - u1(:,[1 1:n-1],:))/2;

   % finite difference approximation for u_y
   u_y = (u1([2:m m],:,:) - u1([1 1:m-1],:,:))/2;

   % Calculate gm*u^(gm-1)*u_x
   lap_x=gm*u1.^(gm-1).*u_x;

   % Calculate gm*u^(gm-1)*u_y
   lap_y=gm*u1.^(gm-1).*u_y;

   % finite difference approximation for lap_x
   lap_xx=(lap_x(:,[2:n n],:) - lap_x(:,[1 1:n-1],:))/2;

   % finite difference approximation for lap_y
   lap_yy = (lap_y([2:m m],:,:) - lap_y([1 1:m-1],:,:))/2;

   % Calculate Laplacian of u^m
   lap_u=lap_xx+lap_yy;

   u1= u1 + dt*(lap_u);
   temp=u1;
end
subplot(1,2,2), imshow(uint8(temp))
str1=sprintf('T=%d',T1);
title(str1);