|   | 
           | 
            |        
         
         
          |   | 
          Volume 8, Issue 1, Article 2 | 
           | 
         
         
           | 
           | 
           | 
           | 
         
       |   | 
             A Sobolev-type Inequality with Applications
 
  | 
          
          |   | 
            | 
          Authors:  | 
          Ramón G. Plaza,  | 
            | 
         
         
          |   | 
            | 
          Keywords: 
             | 
          Sobolev-type inequality, Linear decay rates, Viscous shocks. | 
            | 
         
         
          |   | 
            | 
          Date Received: 
             | 
          02/08/06 | 
            | 
         
         
          |   | 
            | 
          Date Accepted: 
             | 
          09/02/07 | 
            | 
         
         
          |   | 
            | 
          Subject Codes: | 
           
             26D10, 35L67. 
           | 
            | 
          
          |   | 
            | 
          Editors:  | 
          Catherine Bandle,   | 
            | 
         
         
          |   | 
         
         
           | 
           | 
           | 
           | 
           | 
         
         
          |   | 
            | 
          Abstract: | 
           
              In this note, a Sobolev-type inequality is proved. Applications to obtaining linear decay rates for perturbations of viscous shocks are also discussed.
             
          
         |  
         
           | 
           | 
           | 
           | 
           | 
         
         
          |   | 
            | 
            | 
           
           |  
         |  
         
          |   | 
            | 
            | 
           | 
            | 
          
         
         
        |