Nonlinear Degenerate Parabolic Equation with Nonlinear Boundary Condition

In this paper, we obtain the necessary and sufficient conditions on the global existence of all positive （weak） solutions to a nonlinear degenerate parabolic equation with nonlinear boundary condition.     

Fujita Exponent for Porous Medium Equation with Convection and Nonlinear Boundary Condition

This paper is concerned with the critical exponent of the porous medium equation with convection and nonlinear boundary condition. It is shown that the coefficient of the lower order term is an important factor that determines the critical exponent.     

Initial Boundary Value Problem for A Generalized Nonlinear Telegraph Equation with Nonlinear Damping北大核心CSCD

In this paper, the existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the generalized nonlinear telegraph equation with nonlinear damping © 2022 Chinese Academy of Sciences. All rights reserved.     

A Mini Max Theorem for the Functionals with Hemicontinuous Gateaux Derivative and the Solution of the Boundary Value Problem for the Nonlinear Wave Equation

In this paper, a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem.     

Nonlinear Periodic Boundary Value Problem for Second Order Integro-differential Equations of Volterra Type

The periodic boundary value problem for a class of second order nonlinear integro-differential equations are disussed by using the monotone iterative technique. The open problem raised by Lakshmikantham in 1986 is solved.     

Initial–Boundary Value Problem for a Three-Dimensional Equation of the Parabolic-Hyperbolic Type

Differential Equations - We study an initial–boundary value problem for an equation of the mixed parabolic-hyperbolic type in a rectangular parallelepiped. A uniqueness criterion is...     

Boundary Control Problem for a Nonlinear Convection–Diffusion–Reaction Equation

Computational Mathematics and Mathematical Physics - The solvability of boundary-value and extremum problems for a nonlinear convection–diffusion–reaction equation with mixed boundary...     

A Kind of Boundary Element Methods for Boundary Value Problem of Helmholtz Equation

1.Problems for electromagnetic scattering are of significant importance in many areas oftechnology.In this paper we discuss the scattering problem of electromagnetic wave incidentby using boundary element method associated with splines.The problem is modelled by aboundary value problem for the Helmholtz equation     

Initial Boundary Value Problem for One Class of System of Multidimensional Nonlinear Schrodinger-Boussinesq Type Eequations

§1.Introduction In laser-plasma nonlinear interactions, the poblems of solution for oneclass of system of nonlinear Schrodinger-Boussinesq type equations in onedimension have been studied in〔1,2〕. In〔3〕 a class of multidimensionalnonlinear Boussinesq type has been proposed. Under some conditions, wehave proved the existence and uniquenss of the global solution for one     

Sharp Condition for Global Existence of Supercritical Nonlinear Schr?dinger Equation with a Partial Confinement

We study the L²-supercritical nonlinear Schr?dinger equation(NLS) with a partial confinement,which is the limit case of the cigar-shaped model in Bose-Einstein condensate(BEC). By constructing a cross constrained variational problem and establishing the invariant manifolds of the evolution fow, we show a sharp condition for global existence.     

Finite Difference Method of Boundary Problem for Nonlinear Pseudo-Hyperbolic Systems

§1 In the study of the practical problems, such as the forced vibration of plane boundary layer, the transfer of the bioelectric signal in aminal nervous systems and so forth, the linear and nonlinear equations with the main part of form u_(lt)-u_(xxt) of pseudo-hyperbolic type often appear. Many authors have paid attention to solve various problems for the linear and nonlinear pseudo-hyperbolic equations. For a fairly general family of nonlinear pseudo-hyperbolic systems, which contains above mentioned equations as simple special cases, the global solutions of the periodic boundary problems and the initial problems are obtained by Galerkin's method in[7].     

The Initial Boundary Value Problem for Symmetric Long Wave Equations with Nonhomogeneous Boundary Value

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Problem with a Bitsadze–Samarskii Condition on Parallel Characteristics for a Mixed Type Equation of the Second Kind

Differential Equations - For a mixed type equation of the second kind, we prove the uniqueness and existence of a solution of the boundary value problem with the Tricomi condition on part of the...     

Difference Scheme for One Type of Nonlinear Parabolic Equation

We consider the following initial-boundary-value problem of nonlinear parabolic equations Let h denote step size of space and τ denote step size of time. We use the following notation We give the difference scheme for the problem (1)-(2)     

A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation

A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.     

Nonexistence of Global Solutions of a Mixed Problem for a Ginzburg–Landau Type Nonlinear Evolution Equation

Doklady Mathematics - The nonexistence of global solutions of the Dirichlet mixed problem for a nonlinear evolution equation of the Ginzburg–Landau type is studied. For “sufficiently...     

Doubly Degenerate Parabolic Equation with Nonlinear Inner and Boundary Sources

This paper deals with blow-up criterion for a doubly degenerate parabolic equation of the form (un)t = (|ux|m-1ux)x up in (0, 1) × (0, T) subject to nonlinear boundary source (|ux|m-1ux)(1,t) = uq(1,t), (|ux|m-1ux)(0,t) = 0, and positive initial data u(x,0) = uo(x), where the parameters m, n, p, q ＞ 0.It is proved that the problem possesses global solutions if and only if p ≤ n and q≤min{n, m(n 1)/ m 1}.     

Existence of the Global Smooth Solution to the Period Boundary Value Problem of Fractional Nonlinear Schrodinger Equation

It is well known that Feynman and Hibbs[1] used path integrals over Brownian paths to derive the standard(nonfractional) Schrodinger equation. Recently, Laskin[5, 6] showed that the path integral over the Lévy-like quantum mechanical paths allows to develop the generalization of the quantum mechanics. Namely, if the path integral over Brownian trajectories leads to the well known Schrodinger equation, then the path integral over Lévy trajectories leads to the fractional Schrodinger equation. Laskin[7] showed the Hermiticity of the fractional Hamilton operator and established the parity conservation law. Xiaoyi Guo and Mingyu Xu[4] studied some physical applications of the fractional Schrodinger equation.