The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass control, which includes the important cases of mass conservation and mass dissipation. Under these assumptions, the local classical solution is shown to be global, and in the case of mass conservation or mass dissipation, to have the $L^{\infty }$-norm growing at most polynomially in time. Applications include skew-symmetric Lotka-Volterra systems and quadratic reversible chemical reactions.

中文翻译：

---

具有任意维质量控制的二次系统的全局经典解

研究了在任意空间维度上反应扩散系统经典解的整体存在性。假定非线性为准正，具有（略超）二次增长，并具有质量控制，其中包括质量守恒和质量耗散的重要情况。在这些假设下，局部经典解被证明是全局的，并且在质量守恒或质量耗散的情况下，具有${\mathrm{大号}}^{\infty }$-规范最多会随着时间增长。应用包括倾斜对称的Lotka-Volterra系统和二次可逆化学反应。