On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables

 Access to full text

 Full (PDF)

1. Nečas J., Les méthodes directes en théorie aux équations elliptique, Edition de l'Academie tchécoslovaque des sciences, Praha 1967. (1967) 
2. Hlaváček I., Variational Principles for Parabolic equations, Aplikace matematiky 14 (1969), 4, Praha 1969. (1969) MR0255988
3. Wilcox C. H., Linear hyperbolic equations, Arch Rational Mech. and Anal., Vol. 10, Number 5, 1962. (1962) MR0145203
4. Rothe E., 10.1007/BF01782368, Math. Ann. 102 (1930). (1930) MR1512599DOI10.1007/BF01782368
5. Ladyženskaja O. A., Solution of the First Boundary Value Problem for Quasilinear Parabolic Equations, Trudy Mosk. Mat. Obš. 7 (1958). (In Russian.) (1958) MR0114050
6. Iljin A. M., Kalašnikov A. S., Oleinik O. A., Linear Equations of the Second Order of Parabolic Type, Uspechi XVII (1962), 3. (In Russian.) (1962) 
7. Ladyženskaja O. A., On the Solution of Nonstationary Operator Equations, Mat. Sborník 39 (81), No. 4, 1956. (In Russian.) (1956) 
8. Ibragimov Š. I., On the Analogy of the Method of Lines for Differential Equations in Abstract Spaces, Dokl. Azerb. Ak. Nauk XXI, No. 6, 1965. (In Russian.) (1965) MR0192158

1. Komil Kuliev, Lars-Erik Persson, An extension of Rothe's method to non-cylindrical domains
2. Jindřich Nečas, Application of Rothe's method to abstract parabolic equations
3. Karel Rektorys, Marie Ludvíková, A note on nonhomogeneous initial and boundary conditions in parabolic problems solved by the Rothe method
4. Jozef Kačur, Application of Rothe's method to nonlinear evolution equations
5. Jozef Kačur, Alojz Wawruch, On an approximate solution for quasilinear parabolic equations
6. Jozef Kačur, Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order
7. Jozef Kačur, Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
8. Jozef Kačur, Nonlinear parabolic equations with the mixed nonlinear and nonstationary boundary conditions
9. Jozef Kačur, A generalized maximum principle and estimates of max vrai $u$ for nonlinear parabolic boundary value problems
10. Milan Pultar, Solutions of abstract hyperbolic equations by Rothe method.