Errata of Strauss, Partial Differential Equations, second edition
- A list
of corrections from the author's website.
- A few more items.
- Page 42: It should be emphasized that the constant
k in the diffusion equation is positive, i.e. k > 0.
The positivity of k is crucial for the proof of the
maximum principle on page 43 and for both proofs of
uniqueness on page 44.
- Page 50, line 5: replace "as t -> 0" by "as t -> 0^+"
(t approaches 0 right the right, with a plus sign in
superscript next to 0).
- Page 53, problem 14: Need to assume that a>0.
- The equality (3) on page 62 holds for 0 < x < ct, not
0 < x < c |t|.
(Indeed if t <0 and 0 < x < -c t, then
φ(ct+x) and φ(ct-x) do not make sense, since the
function &phi is defined on the half line of all positive
real numbers.)
For 0 < x < -c t,
v(x,t)= (1/2) [-φ(-x-ct) + φ(x-ct)]
+ (1/2c)\int_{-x-ct}^{x-ct}ψ(y)dy .
(Here we have followed convention in LaTeX codes, and
\int_{-x-ct}^{x-ct}ψ(y)dy
denotes the integral of ψ from x+ct to x-ct.)
- page 69: On line 7, the limit as s -> t should be s -> t^-
(s approaches t from the left, with a minus sign in
superscript next to t). Similarly, 4 lines down,
ε ->0^+ (ε approaches 0 from the right).
- page 157: In the calculation of the Laplace operator
in polar coordinate, there are errors on lines -6 and -9.
In coefficients of \frac{\partial}{\partial\theta} for
\frac{\partial^2}{\partial x^2} and
\frac{\partial^2}{\partial y^2},
the factor "2" should be eliminated (i.e. the correct
factor is "1" instead of "2").
(Here \frac{\partial}{\partial\theta} denotes the partial
derivative with respect to \theta, and
\frac{\partial^2}{\partial x^2} denotes the second partial
derivative with respect to x.)
- page 270, first line of Exercise 1: with initial conditions
(25), not (26).
- Equation (3) on page 234:
change u(x, t_0) to u(x_0, t_0).
- Line -3 of page 307: insert "linearly independent" between "set
of" and "trial".
- Line 2 of page 359: insert a minus sign after the equality in
the continuity equation; See exercise 13.1, problem 1 on page 361.
- There are two typos on page 374. In the displayed formula for
the 4x4 matrix γj, j=1, 2, 3, the 2x2 block in the
upper-right corner should be σj, not
-σj.
In the displayed formula (4) a few lines after,
the conjugate transpose of γj is
-γj for j=1, 2, 3. (In other words, insert a minus
sign between "=" and "γj".)
[Otherwise the equations (5), (6) will not hold.]
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