相关论文: Cauchy problem in the non-classical treatment for …

In the paper the Dirichlet problem with non-classical conditions not requiring agreement conditions is considered for a fourth order pseudoparabolic equation with non-classical coefficients. The equivalence of these conditions with the…

A problem with non-classical conditions on all the boundary not requiring agreement conditions is considered for a sixth order pseudoparapolic equation. The equivalence of these conditions with the classic boundary condition is…

In the paper the Goursat problem with non classical boundary conditions not requiring the agreement conditions is considered for a sixth order pseudoparabolic equation with the classical boundary condition is substantiated in the case if…

For this equation we consider a final-boundary value problem with non-classical conditions not requiring agreement conditions. Equivalence of these conditions with the classic boundary condition is substantiated in the case if the solution…

The Cauchy problem is investigated for the parabolic type in the some finite part $[t_0, t_1] \subset [0, \infty)$ of the semi axis $t \in [0, \infty)$ and degenarated to Schrodinger type in the remain part of the same semi axes the second…

In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the…

The paper studies some ill-posed boundary value problems on semi-plane for parabolic equations with homogenuous Cauchy condition at initial time and with the second order Cauchy condition on the boundary of the semi-plane. A class of inputs…

We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic…

We consider a Cauchy problem for a fractional anisotropic parabolic equation in anisotropic H\"{o}lder spaces. The equation generalizes the heat equation to the case of fractional power of the Laplace operator and the power of this operator…

We consider the Cauchy problem for a class of nonlinear degenerate parabolic equa- tion with forcing. By using the vanishing viscosity method we obtain generalized solutions. We prove some regularity results about this generalized…

We consider the Cauchy problem for a second order quasi-linear partial differential equation with an admissible parabolic degeneration such that the given functions described the initial conditions are defined on a closed interval. We study…

We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…

Parabolic integro-differential non degenerate Cauchy problem is considered in the scale of H\"older spaces of functions whose regularity is defined by a radially O-regularly varying L\'evy measure. Existence and uniqueness and the estimates…

Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is…

In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transition density functions of Markov processes in the four…

We consider a quasilinear parabolic Cauchy problem with spatial anisotropy of orthotropic type and study the spatial localization of solutions. Assuming the initial datum is localized with respect to a coordinate having slow diffusion rate,…

We analyse an algorithm of transition between Cauchy problems for second-order wave equations and first-order symmetric hyperbolic systems in case the coefficients as well as the data are non-smooth, even allowing for regularity below the…

In this paper we study the Cauchy problem for second order strictly hyperbolic operators when the coefficients of the principal part are not Lipschitz continuous, but only "Log-Lipschitz" with respect to all the variables. This class of…

We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…

Several negative results are presented concerning the solvability in Sobolev classes of the Cauchy problem for the inhomogeneous second-order uniformly parabolic equations without lower order terms in one space dimension. The main…