Blow up, exponential decay of solutions for a g-heat equation with source term : analytical and numerical results
Resumo
We consider an initial value problem related to the equation (1.1), with homogeneous Diriclet boundary condition in a bounded domain.We prove under suitable conditions on initial energy a blow up and exponential decay of solutions, and also give the numerical examples to illustrate the blow up and exponential decay results.
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Referências
M. G. Crandall, H. Ishii andP.L. Lions, User’s guide to viscosity solutions of second order partial differential equations, Bulletin of the American Mathematical Society, Vol. 27, No. 1, (1992), 1–67.
V. Komornik, Exact controllability and stabilization the multiplier method. Paris: Masson-JohnWiley, 1994.
S. Larson, V. Thomee, Partial Differential Equations with Numerical Methods, Text in Applied Mathematics, Springer, 2009.
S. A. Messaoudi, Blow-up of solutions of a semilinear heat equation with a Visco-elastic term, Progress in Nonlinear Differential Equations and Their Applications, 64(2005), 351-356.
A. Ouaoua, A. Khaldi and M. Maouni, Stabilization of solutions for a Kirchhoff type reaction-diffusion equation. Canad. J. Appl. Math. 2 (2020), 71-80.
A. Ouaoua, M. Maouni, Blow-up, exponential growth of solution for a nonlinear parabolic equation with p(x)-Laplacian, International Journal of Analysis and Applications. 17 (2019), 620-629.
M. Otani, Nonmonotone perturbations for nonlinear parabolic equations associated with subdi erential operators, Cauchy problems, J. Differential Equations 46 (1982), 268-299.
S, Peng, A generalized dynamic programming principle and Hamilton-Jacobi-Bellman equation, Stochastics and Stochastic Reports, Vol. 38, No. 2, (1992), 119–134.
S, Peng, Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, English Series 20(2), (2004), 1–24.
S, Peng, G-expectation, G-Brownian motion and related stochastic calculus of Ito type , in Benth et al. (Eds.): Stochastic Analysis and Applications, The Abel Symposium 2005, Abel Symposia 2, (2005), 541–567, Springer-Verlag.
S, Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation , Stochastic Processes and their Applications, Vol. 118, No. 12, (2008), 2223–2253.
S, Peng, Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations, Sci. China Ser. A, Vol. 52, No. 7, (2009), 1391–1411.
N. Polat, Blow up of solution for a nonlinear reaction diffusion equation with multiple nonlinearities, Int. J. Sci. Technol. 2 (2) (2007), 123-128.
P. Pucci and J. Serrin, Asymptotic stability for nonlinear parabolic systems, Energy Methods in Continuum Mechanics (Oviedo, 1994), Kluwer Academic Publishers, Dordrecht, (1996),.66-74.
A. Quarteroni, A. Valli, Numerical Approximation of Partial Differential Equations, SCM Series no. 23, Springer-Verlag, Heidelberg, 1994.
A. Quarteroni, R. Sacconand F. Saleri, Numerical Mathematics, second ed., TAM Series no. 37, 2000, Springer-Verlag, New-York, 2007.
J. Yong and X. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999.
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