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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1993 • Question 23

Question

Math 6410 • ODE Fall 1993 • Question 23

Use the above to establish the existence and uniqueness of solutions to the initial value problem \[ U_t=U_{xx}+f(t,x),\quad t>0,\quad x\in (0,1) \] \[ U(0,x)=\varphi (x) \] \[ U(t,0)=U(t,1)=0; \] be sure to provide the appropriate function spaces for \(U\), \(f\), \(\varphi \).

Raw LaTeX

Use the above to establish the existence and uniqueness of solutions to
the initial value problem
\[
U_t=U_{xx}+f(t,x),\quad t>0,\quad x\in(0,1)
\]
\[
U(0,x)=\varphi(x)
\]
\[
U(t,0)=U(t,1)=0;
\]
be sure to provide the appropriate function spaces for \(U\), \(f\), \(\varphi\).

Topic Tags

Existence and Uniqueness Theorems Global Existence and Finite-Time Blow-Up Heat Equation and Parabolic Equations Poincare Maps and Periodic Solutions