All Partial Differential Equations Resources
Example Questions
Example Question #3 : Partial Differential Equations
Determine if the statement is true or false:
The wave equation has at most one solution.
Possible Answers:
False
True
Correct answer:
True
Explanation:
This statement is true by the Uniqueness Theorem.
is twice differential equation in terms of
and
.
Now, consider the energy integral
After performing integration by parts results in the following,
From here, the initial conditions and boundary conditions are applied.
Therefore,
which proves the wave equations has only one solution and thus is unique.
All Partial Differential Equations Resources
Popular Subjects
Math Tutors in New York City, SAT Tutors in Philadelphia, GRE Tutors in Seattle, Algebra Tutors in Denver, ISEE Tutors in Phoenix, LSAT Tutors in Denver, Physics Tutors in Denver, SSAT Tutors in Chicago, ISEE Tutors in Philadelphia, Math Tutors in Seattle
Popular Courses & Classes
MCAT Courses & Classes in Philadelphia, LSAT Courses & Classes in San Diego, SSAT Courses & Classes in Miami, ISEE Courses & Classes in San Francisco-Bay Area, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in Denver, GRE Courses & Classes in San Diego, ACT Courses & Classes in Phoenix, MCAT Courses & Classes in Boston, SSAT Courses & Classes in San Diego
Popular Test Prep
LSAT Test Prep in Philadelphia, SAT Test Prep in Chicago, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Miami, MCAT Test Prep in Atlanta, LSAT Test Prep in Boston, ISEE Test Prep in Los Angeles, ISEE Test Prep in New York City, SAT Test Prep in Los Angeles, MCAT Test Prep in Washington DC
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)