## Quasilinear first-order equations with continuous nonlinearities.(English. Russian original)Zbl 0880.35027

Russ. Acad. Sci., Dokl., Math. 50, No. 3, 391-396 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 339, No. 2, 151-154 (1994).
The paper presents theorems on comparison and maximum principles, uniqueness and existence of generalized entropy solution to the equation $$u_t+\text{div}_xf(u)= g(x)$$, resp. $$u_t+\text{div}_x f(u)=g(t,x)$$, where $$x\in\mathbb{R}^n$$, $$0< t\leq T$$, $$u\in \mathbb{R}$$ and $$f= (f_1,\dots,f_n)$$ is in a certain sense anisotropic.
Reviewer: A.Doktor (Praha)

### MSC:

 35F25 Initial value problems for nonlinear first-order PDEs 35D05 Existence of generalized solutions of PDE (MSC2000) 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B50 Maximum principles in context of PDEs

### Keywords:

generalized entropy solution