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Question: How to solve this PDE system ?

Question:How to solve this PDE system ?

Prakash J 100 Maple 2018
homework pde differential-equations initial-conditions incomplete-question
May 18 2023
0

eq1:=( d)/(dt)u+(d^(2))/(dy^(2))u + s*( d)/(dy)u + delta * theta = 0;

eq2:=( d)/(dt)theta + (d^(2))/(dy^(2))theta + s*Pr*( d)/(dy)theta +lambda* exp(theta/(1 +(epsilon*theta))) = 0; 

initial and boundary conditons   

t <=0; u = theta = 0, for 0 <= y  <= 1   

t> 0;  u =0, theta = 0   at  y = 0;  

t> 0;  u =1, theta = 0   at   y = 1  ;

where, s, epsilon, Pr, lambda, delta are arbitrary parameters
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