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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
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