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arXiv · 1908.02961

Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities

Desheng Li
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Abstract

This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\frac{\patial u}{\patial t}-\Delta u=f(x,u)+g(u(x,t-r_1(t)),\cdots,u(x,t-r_m(t)))+h(x,t)$$ in a bounded domain $\Omega\subset R^n$ with fast-growing nonlinearities and a dissipative structure, which is associated with the homogeneous Dirichlet boundary condition. Our results reveal some deeper inherent connections between dissipative structures and the regularity of solutions for such problems.

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Desheng Li. 2019-08-08. Global Estimates and Regularity of Retarded Parabolic Equations with Fast-growing Nonlinearities. https://arxiv.org/abs/1908.02961

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