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On The Initial Value Problem For The Quasi-Linear Parabolic Partial Differential Equation, Henry Hermes
On The Initial Value Problem For The Quasi-Linear Parabolic Partial Differential Equation, Henry Hermes
Mathematics & Statistics ETDs
In this paper we consider second order parabolic partial differential equations on the infinite strip. We confine our attention to the quasi-linear equations, and in particular, the problem
(0-1) u͙(t,x) = f(u)uxx(t.x) , (t,x) ε(0,T)x(-∞,∞) ≡ DT, T>0
u(0,x) = u0(x) , x ε (-∞,∞).
Existence, uniqueness and properties of the solution are discussed. These results can be immediately generalized to problems where the differential equation is of the form u͙(t,x) = f(t,x,u)u xx(t,x).