Related papers: Second order formulation of boundary value problem…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
We prove the first positive results concerning boundary value problems in the upper half-space of second order parabolic systems only assuming measurability and some transversal regularity in the coefficients of the elliptic part. To do so,…
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
In this study, we found a regular trace formula for the eigenvalues of the boundary value problem, which we created with the second-order differential equation with eigen parameter and discontinuity at x ={\pi}/2, which is an interior point…
Conditions of the existence of solutions of linear and perturbed linear boundary value problems in the Hilbert spaces for the second order evolution equation are obtained.
We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the initial condition corresponds to an impasse point of the…
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
In this paper the boundary value problem for one class of the operator-differential equations of the third order on a semi-axis, where one of the boundary conditions is perturbed by some linear operator is researched. There are received…
We propose a natural gradient term for a class of second-order partial differential equations of the form \begin{equation}\nonumber M(x,Du,D^2u)+g(u)N(x,Du, D^2u)+f(x,u)=0 \;\;\mbox{in}\;\; \Omega, \end{equation} where…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…
Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
To solve numerically boundary value problems for parabolic equations with mixed derivatives, the construction of difference schemes with prescribed quality faces essential difficulties. In parabolic problems, some possibilities are…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
Initial-boundary value problems for second order fully nonlinear PDEs with Caputo time fractional derivatives of order less than one are considered in the framework of viscosity solution theory. Associated boundary conditions are Dirichlet…
In this paper, we prove that there exists a unique weak solution to the mixed boundary value problem for a general class of semilinear second order elliptic partial differential equations with singular coefficients. Our approach is…
We consider second order elliptic divergence form systems with complex measurable coefficients $A$ that are independent of the transversal coordinate, and prove that the set of $A$ for which the boundary value problem with $L_2$ Dirichlet…