Solvability problem for strong-nonlinear nondiagonal parabolic system

Arina A. Arkhipova

Mathematica Bohemica (2002)

  • Volume: 127, Issue: 2, page 131-138
  • ISSN: 0862-7959

Abstract

top
A class of q -nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities q ( 1 , 2 ) , q = 2 , q > 2 , are analyzed.

How to cite

top

Arkhipova, Arina A.. "Solvability problem for strong-nonlinear nondiagonal parabolic system." Mathematica Bohemica 127.2 (2002): 131-138. <http://eudml.org/doc/249042>.

@article{Arkhipova2002,
abstract = {A class of $q$-nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities $q\in (1,2)$, $q=2$, $q>2$, are analyzed.},
author = {Arkhipova, Arina A.},
journal = {Mathematica Bohemica},
keywords = {boundary value problems; nonlinear parabolic systems; solvability; strong nonlinearities in the gradient},
language = {eng},
number = {2},
pages = {131-138},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Solvability problem for strong-nonlinear nondiagonal parabolic system},
url = {http://eudml.org/doc/249042},
volume = {127},
year = {2002},
}

TY - JOUR
AU - Arkhipova, Arina A.
TI - Solvability problem for strong-nonlinear nondiagonal parabolic system
JO - Mathematica Bohemica
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 127
IS - 2
SP - 131
EP - 138
AB - A class of $q$-nonlinear parabolic systems with a nondiagonal principal matrix and strong nonlinearities in the gradient is considered.We discuss the global in time solvability results of the classical initial boundary value problems in the case of two spatial variables. The systems with nonlinearities $q\in (1,2)$, $q=2$, $q>2$, are analyzed.
LA - eng
KW - boundary value problems; nonlinear parabolic systems; solvability; strong nonlinearities in the gradient
UR - http://eudml.org/doc/249042
ER -

References

top
  1. Linear and Quasilinear Equations of Parabolic Type, Amer. Math Society, Providence, 1968. (1968) 
  2. Some (new) counterexamples of parabolic systems, Comment. Math. Univ. Carolin. 36 (1995), 503–510. (1995) MR1364491
  3. 10.1007/BF01161997, Math. Z. 201 (1989), 83–103. (1989) MR0990191DOI10.1007/BF01161997
  4. 10.1016/S0294-1449(16)30316-X, Ann. Inst. Henri Poincare 6 (1989), 363–395. (1989) Zbl0687.58004MR1030856DOI10.1016/S0294-1449(16)30316-X
  5. Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables, Probl. Mat. Anal., St. Petersburg Univ. 16 (1997), 3–40. (1997) Zbl0953.35059MR1668390
  6. Local and global solvability of the Cauchy-Dirichlet problem for a class of nonlinear nondiagonal parabolic systems, St. Petersburg Math. J. 11 (2000), 989–1017. (2000) Zbl0973.35095MR1746069
  7. Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic growth nonlinearities. I. On the continuability of smooth solutions, Comment. Math Univ. Carolin. 41 (2000), 693–718. (2000) Zbl1046.35047MR1800172
  8. Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic growth nonlinearities. II. Local and global solvability results, Comment. Math. Univ. Carolin. 42 (2001), 53–76. (2001) MR1825372

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.