Consider the Problem of Finding the Temperature in a Semi-Infinite $u _ { 0 }$

Multiple Choice

Consider the problem of finding the temperature in a semi-infinite rod with zero initial temperature and a fixed constant temperature, $u _ { 0 }$ , at $x = 0$ . The mathematical model for this problem is

A) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( x , 0 ) = 0 , u ( 0 , t ) = u _ { 0 }$
B) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( x , 0 ) = 0 , u ( 0 , t ) = u _ { 0 }$
C) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial t } = 0 , u ( x , 0 ) = 0 , u ( 0 , t ) = u _ { 0 }$
D) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = 0 , u ( x , 0 ) = u _ { 0 } , u ( 0 , t ) = 0$
E) $k \frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial t } = 0 , u ( x , 0 ) = u _ { 0 } , u ( 0 , t ) = 0$