相关论文: Existence and uniqueness of solutions for a nonloc…

In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and…

We analyze the asymptotic behavior corresponding to the arbitrary high conductivity of the heat in the thermoelectric devices. This work deals with a steady-state multidimensional thermistor problem, considering the Joule effect and both…

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information…

In this paper we prove uniqueness results for renormalized solutions to a class of nonlinear parabolic problems.

We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schr\"odinger equation with a potential, and the heat equation with a variable…

We consider the heat equation in a multidimensional domain with nonlocal hysteresis feedback control in a boundary condition. Thermostat is our prototype model. We construct all periodic solutions with exactly two switching on the period…

We prove a few existence results of a solution for a static system with a coupling of thermoviscoelastic type. As this system involves $L^1$ coupling terms we use the techniques of renormalized solutions for elliptic equations with $L^1$…

In this paper, we consider the Cauchy problem for the Hardy parabolic equation with general nonlinearity and establish the local existence and nonexistence results. Our results provide the optimal integrability conditions on initial…

Global well-posedness of the time-dependent (degenerate) thermistor problem remains open for many years. In this paper, we solve the problem by establishing a uniform-in-time BMO estimate of inhomogeneous parabolic equations. Applying this…

We prove some uniqueness results for weak solutions to some classes of parabolic Dirichlet problems.

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the…

We develop estimates for the solutions and derive existence and uniqueness results of various local boundary value problems for Dirac equations that improve all relevant results known in the literature. With these estimates at hand, we…

We prove existence, uniqueness and regularity of solutions of nonlocal heat equations associated to anisotropic stable diffusion operators. The main features are that the right-hand side has very few regularity and that the spectral measure…

We study the existence of global-in-time solutions for a nonlinear heat equation with nonlocal diffusion, power nonlinearity and suitably small data (either compared pointwisely to the singular solution or in the norm of a critical Morrey…

We give a proof of existence and uniqueness of viscosity solutions to parabolic quasilinear equations for a fairly general class of nonconvex Hamiltonians with superlinear growth in the gradient variable. The approach is mainly based on…

We consider a class of elliptic and parabolic problems, featuring a specific nonlocal operator of fractional-laplacian type, where integration is taken on variable domains. Both elliptic and parabolic problems are proved to be uniquely…

We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.

In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…

In this paper we consider a semilinear parabolic equation with nonlinear and nonlocal boundary condition and nonnegative initial datum. We prove some global existence results. Criteria on this problem which determine whether the solutions…

We consider the Cauchy problem for a system of fully nonlinear parabolic equations. In this paper, we shall show the existence of global-in-time solutions to the problem. Our condition to ensure the global existence is specific to the fully…