On the stability of solutions for a family of parabolic equations with time delay on $${\mathbb {R}}^n$$

Autor: Almaz Butaev
Rok vydání: 2019
Předmět:
Zdroj: Complex Analysis and its Synergies. 5
ISSN: 2197-120X
2524-7581
DOI: 10.1007/s40627-019-0029-1
Popis: In this paper we consider the following initial value problem $$\begin{aligned} \left\{ \begin{array}{ll} (\partial _t - \Delta _x + w\cdot \nabla _x +\alpha I) u(t,x) - \beta u(t-\tau ,x) = 0, &{} (t,x)\in {\mathbb {R}}_+\times {\mathbb {R}}^n \\ u(t,x) = \phi (t,x)\in C([-\tau ,0],L^1({\mathbb {R}}^n)) &{} \end{array} \right. \end{aligned}$$ We describe the ranges of the parameters $$\alpha , \beta ,\tau $$ that guarantee that every solution u(t, x) vanishes as $$t\rightarrow \infty $$ .
Databáze: OpenAIRE
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