# I. I. Kovtun

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Articles: 2

### Boundary problems and initial-boundary value problems for one class of nonlinear parabolic equations with Lévy Laplacian

Methods Funct. Anal. Topology 17 (2011), no. 2, 118-125

We develop a method to construct a solution to a boundary problem and an initial-boundary value problem in a fundamental domain of a Hilbert space for a class of nonlinear parabolic equations not containing explicitly the unknown function, $$\frac{\partial U(t,x)}{\partial t}=f(t,\Delta_LU(t,x)),$$ where $\Delta _L$ is the infinite dimensional Lévy Laplacian.

### Quasilinear parabolic equations with a Lévy Laplacian for functions of infinite number of variables

Methods Funct. Anal. Topology 14 (2008), no. 2, 117-123

We construct solutions to initial, boundary and initial-boundary value problems for quasilinear parabolic equations with an infinite dimensional Lévy Laplacian $\Delta _L$, $$\frac{\partial U(t,x)}{\partial t}=\Delta_LU(t,x)+f_0(U(t,x)),$$ in fundamental domains of a Hilbert space. The solution is defined in the functional class where a solution of the corresponding problem for the heat equation $\frac {\partial U(t,x)}{\partial t}=\Delta_LU(t,x)$ exists.