<h3>MA6007 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS</h3>
<br/>
<h4>Course Details</h4>
Review of first order equations and characteristics<br> Weak solutions to hyperbolic equations- discontinuous solutions, shock formation, a formal approach to weak solutions, asymptotic behaviour of shocks<br> Diffusion Processes-Similarity methods, Fisher's equation, Burgers' equation, asymptotic solutions to Burgers' equations<br> Reaction diffusion equations-traveling wave solutions, existence of solutions, maximum principles and comparison theorem, asymptotic behaviour<br> Elliptic equations-Basic results for elliptic operators, eigenvalue problems, stability and bifurcation<br> Hyperbolic system
<br/>
<h4>Course References:</h4>
Books:<br>
J David Logan, An introduction to nonlinear partial differential equations, John Wiley and Sons, Inc., 1994