Question: Problem to solve system of linear PDEs with BSc and ICs


Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response. 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

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