On the solution of the heat equation with nonlinear unbounded memory
Applications of Mathematics, Tome 30 (1985) no. 6, pp. 461-474.

Voir la notice de l'article dans Czech Digital Mathematics Library

The paper deals with the question of global solution $u,\tau$ to boundary value problem for the system of semilinear heat equation for $u$ and complementary nonlinear differential equation for $\tau$ ("thermal memory"). Uniqueness of the solution is shown and the method of successive approximations is used for the proof of existence of a global solution provided the condition $(\Cal P)$ holds. The condition $(\Cal P)$ is verified for some particular cases (e. g.: bounded nonlinearity, homogeneous Neumann problem (even for unbounded nonlinearities), apriori estimate of the solution holds).
DOI : 10.21136/AM.1985.104175
Classification : 35A05, 35K20, 35K55, 35K60
Mots-clés : heat equation; nonlinear unbounded memory; uniqueness; existence; boundary value problem 
@article{10_21136_AM_1985_104175,
     author = {Doktor, Alexandr},
     title = {On the solution of the heat equation with nonlinear unbounded memory},
     journal = {Applications of Mathematics},
     pages = {461--474},
     publisher = {mathdoc},
     volume = {30},
     number = {6},
     year = {1985},
     doi = {10.21136/AM.1985.104175},
     mrnumber = {0813534},
     zbl = {0602.35056},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104175/}
}
TY  - JOUR
AU  - Doktor, Alexandr
TI  - On the solution of the heat equation with nonlinear unbounded memory
JO  - Applications of Mathematics
PY  - 1985
SP  - 461
EP  - 474
VL  - 30
IS  - 6
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104175/
DO  - 10.21136/AM.1985.104175
LA  - en
ID  - 10_21136_AM_1985_104175
ER  - 
%0 Journal Article
%A Doktor, Alexandr
%T On the solution of the heat equation with nonlinear unbounded memory
%J Applications of Mathematics
%D 1985
%P 461-474
%V 30
%N 6
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104175/
%R 10.21136/AM.1985.104175
%G en
%F 10_21136_AM_1985_104175
Doktor, Alexandr. On the solution of the heat equation with nonlinear unbounded memory. Applications of Mathematics, Tome 30 (1985) no. 6, pp. 461-474. doi : 10.21136/AM.1985.104175. https://geodesic-test.mathdoc.fr/articles/10.21136/AM.1985.104175/

Cité par Sources :