Geodesic
Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions
Nguyen Thanh Long1 ; Nguyen Van Y2 ; Le Thi Phuong Ngoc3
1 Department of Mathematics and Computer Science University of Natural Science Vietnam National University Ho Chi Minh City 227 Nguyen Van Cu St., Dist. 5 Ho Chi Minh City, Vietnam
2 Department of Fundamental Sciences Ho Chi Minh City University of Food Industry 140 Le Trong Tan Str., Tay Thanh Ward, Tan Phu Dist. Ho Chi Minh City, Vietnam and Department of Mathematics and Computer Science University of Natural Science Vietnam National University Ho Chi Minh City 227 Nguyen Van Cu St., Dist. 5 Ho Chi Minh City, Vietnam
3 University of Khanh Hoa 01 Nguyen Chanh St. Nha Trang City, Vietnam
Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 121-145.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider a nonlinear heat equation with a viscoelastic term and Robin conditions. First, we prove existence and uniqueness of a weak solution. Next, we prove that any weak solution with negative initial energy will blow up in finite time. Finally, we give a sufficient condition for the global existence and exponential decay of weak solutions. The main tools are the Faedo–Galerkin method and defining a modified energy functional together with the technique of Lyapunov functional.
DOI : 10.4064/ap4084-3-2017
Keywords: consider nonlinear heat equation viscoelastic term robin conditions first prove existence uniqueness weak solution prove weak solution negative initial energy blow finite time finally sufficient condition global existence exponential decay weak solutions main tools faedo galerkin method defining modified energy functional together technique lyapunov functional

Nguyen Thanh Long 1 ; Nguyen Van Y 2 ; Le Thi Phuong Ngoc 3

1 Department of Mathematics and Computer Science University of Natural Science Vietnam National University Ho Chi Minh City 227 Nguyen Van Cu St., Dist. 5 Ho Chi Minh City, Vietnam
2 Department of Fundamental Sciences Ho Chi Minh City University of Food Industry 140 Le Trong Tan Str., Tay Thanh Ward, Tan Phu Dist. Ho Chi Minh City, Vietnam and Department of Mathematics and Computer Science University of Natural Science Vietnam National University Ho Chi Minh City 227 Nguyen Van Cu St., Dist. 5 Ho Chi Minh City, Vietnam
3 University of Khanh Hoa 01 Nguyen Chanh St. Nha Trang City, Vietnam 
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     title = {Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and {Robin} conditions},
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Nguyen Thanh Long; Nguyen Van Y; Le Thi Phuong Ngoc. Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions. Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 121-145. doi : 10.4064/ap4084-3-2017. http://geodesic.mathdoc.fr/articles/10.4064/ap4084-3-2017/

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