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Generally the PDEs in matlab follow the general formuale :
Where the s is the source term and f is the flux term.
given a PDE , you have to make an analogy between your equation and the general form above, so for example in your case we have : s=0; m=0;c=1; and f=u^0.8*Diveregence(u) .
You have missing conditions in your problem : Initial conditions and Boundary conditions , i tried to write for you the sample with default conditions in Math(c) documentation , adapt it based on you I.C:
% function ( M-file)
function SOL=PDEX1() r=linspace(0,5,100); t=linspace(0,30,100); m=0; SOL= pdepe(m,@pdex1pde,@pdex1ic,@pdex1bc,r,t); function [c,f,s] = pdex1pde(r,t,u,M) % du/dt=div(u^(0.8)du/dr) c =1; D=gradient(u); M =(u.^(0.8)).*D; f= M; s =0; function u0 = pdex1ic(r) u0 = sin(pi*r); function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t) pl = ul; ql = 0; pr = pi * exp(-t); qr = 1;
change now the initial/ boundary conditions.
Your equation seems like it has a Nusselt number no? anyway we r waiting for the result interpretation,
% In the workspace try : >>S=PDEX1(); >>surf(S);
I hope this helps.