Q: Как задать border-bottom радиальный градиент, чтобы получился примерно такой результат? 
Каким образом это можно реализовать?

A: Можно бордером.


.my-div {
  text-align: center;
  width: 600px;
  border-left: none; 
  border-right: none; 
  border-top: none;
  border-bottom: 2px solid;
  border-image: linear-gradient(to right, #ffffff, #90acaa, #6A9393, #ffffff ) 47% 0%;
}
<div class="my-div">Some content</div>



A: Используйте css.


.my-div {
  position: relative;
  text-align: center;
  width: 300px;
}
.my-div::after {
  content: '';
  width: 100%;
  position: absolute;
  left: 0;
  bottom: -1px;
  height: 1px;
  background: #333;
  background: -webkit-gradient(linear, left top, right top, color-stop(0%, hsla(0, 0%, 0%, 0)), color-stop(50%, hsla(0, 0%, 0%, .75)), color-stop(100%, hsla(0, 0%, 0%, 0)));
  background: -webkit-linear-gradient(left, hsla(0, 0%, 0%, 0) 0%, hsla(0, 0%, 0%, .75) 50%, hsla(0, 0%, 0%, 0) 100%);
  background: -moz-linear-gradient(left, hsla(0, 0%, 0%, 0) 0%, hsla(0, 0%, 0%, .75) 50%, hsla(0, 0%, 0%, 0) 100%);
  background: -ms-linear-gradient(left, hsla(0, 0%, 0%, 0) 0%, hsla(0, 0%, 0%, .75) 50%, hsla(0, 0%, 0%, 0) 100%);
  background: -o-linear-gradient(left, hsla(0, 0%, 0%, 0) 0%, hsla(0, 0%, 0%, .75) 50%, hsla(0, 0%, 0%, 0) 100%);
  background: linear-gradient(left, hsla(0, 0%, 0%, 0) 0%, hsla(0, 0%, 0%, .75) 50%, hsla(0, 0%, 0%, 0) 100%);
}
<div class="my-div">Some content</div>


Результат

