Weak solutions of initial-boundary value problems for class of nonlinear viscoelastic equations

References

• Andrews , G. 1980 . On the Existence of Solutions to the Equation utt = uXXt + σ(uX)X . Journal of Differential Equations , 35
   Google Scholar
• Dafermos , C. 1969 . The Mixed Initial-Boundary Value Problem for the Equations of Nonlinear One-Dimensional Visco-elasticity . Journal of Differential Equations , 6 : 71 – 86 .
   Google Scholar
• Greenberg , J.M. 1969 . On the Existence, Uniqueness, and Stability of the Equation ρ X = E(X )X + AX . J. Math. Anal. Appl , 25 : 575 – 591 .
   Google Scholar
• Greenberg , J.M. and Mc Camey , R.C. 1970 . On the Exponential Stability of Solutions of E(u X)uXX + λuXtX . J. Math. Anal. Appl , 25 : 406 – 417 .
   Google Scholar
• Greenberg , J.M. , Mc Camey , R.C. and Mizel , V.J. 1968 . On the Existence, Uniqueness and stability of solutions of the equation σ'(u ) uXX + λuxxt = ρ0utt . J. Math. Mech , 17 : 707 – 728 .
   Web of Science ®Google Scholar
• Hicks , D.L. 1979 . the Hydrocode Convergence Problem - Part 2 . Comp. Math in Appl. Mech. and Engr , 20 : 303 – 316 .
   Google Scholar
• Kanel , Ya . 1966 . On Some Systems of Quasilinear Parabolic Equations, English Transl. in USSR . Comp. Math, and Math. Physics , 6 : 74 – 88 .
   Google Scholar
• Ya Kanel . 1968 . On a Model System of Equations of One Dimensional Gas Motion English Transl . in Diff. Eqns , 4 : 374 – 380 .
   Google Scholar
• Kazhikhov , A.V. 1975 . Correctness "in the large" of Initial-Boundary Value Problems for Model Systems of Equations of Viscous Gas . Din. Sploshnoi Sredy , 21 : 18 – 47 . In Russian
   Google Scholar
• Kazhikhov , A.V. and Nikolaev , V.B. 1979 . On the Correctness of Boundary Value Problems for the Equations of a Viscous Gas with a Non-monotonic Function of State . Chislennye Metody Mekh. Sploshnoi Sredy , 10 : 77 – 84 . In Russian
   Google Scholar
• Kuttler , K. and Hicks , D. 1979 . Initial-Boundary Value Problems for Some Nonlinear Conservation Laws . to appear in Applicable Analysis , 10
   Google Scholar
• Kuttler , K. Regularity of Weak Solutions of Some Nonlinear Conservation Laws, submitted ,
   Google Scholar
• Showalter , R.E. 1977 . Hilbert Space Methods for Partial Differential Equations , Pitman .
   Google Scholar
• Solonikov , V.A. and Kazhikhov , A.V. 1981 . Existence Theorems for the Equations of Motion of a Compressible Viscous Fluid . Annual Review of Fluid Mechanics , 13 : 79 – 95 .
   Google Scholar
• Gilbarg , D. and Trudinger , N.S. 1977 . Elliptic Partial Differential Equations of Second Order , Springer-Verlag .
   Google Scholar