Boundary-Value Problems for a Third-Order Loaded Parabolic-Hyperbolic Equation with Variable Coefficients (original) (raw)

A Class of Third Order Parabolic Equations with Integral Conditions

2009

In this paper, we study a mixed problem for a third order parabolic equation with non classical boundary condition. We prove the existence and uniqueness of the solution. The proof of the uniqueness is based on a priori estimate and the existence is established by Fourier’s method. Mathematics Subject Classification: 35B45, 35K35

On nonlinear integro-differential equations of hyperbolic type

Nonlinear Analysis: Theory, Methods & Applications, 2009

This paper considers unified initial-boundary value problems for integro-differential equations of hyperbolic type. For such problems where the forcing functions satisfy certain monotonicity conditions, monotone sequences converging to coupled minimal-maximal solutions may be constructed from a single pair of coupled lower-upper solutions. The coupled minimal-maximal solutions coincide in a unique solution provided the problem satisfies certain one-sided Lipschitz conditions.

A computational method for integro-differential hyperbolic equation with integral conditions

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, 2013

The aim of this paper is to prove existence, uniqueness, and continuous dependence upon the data of solution to hyperbolic equation with purely integral conditions. The proofs are based on a priori estimate and Laplace transform method. Finally, we obtain the solution by using a numerical technique for inverting the Laplace transforms.

Existence and Uniqueness of the Solution for Volterra-Fredholm Integro-Differential Equations

Journal of Siberian Federal University. Mathematics & Physics, 2018

In this article, modified Adomian decomposition method is successfully applies to find the approximate solutions of Volterra-Fredholm integro-differential equations. Moreover, we prove the existence and uniqueness results and convergence of the solutions. Finally, an example is included to demonstrate the validity and applicability of the proposed technique. Keywords: Modified Adomian decomposition method, Volterra-Fredholm integro-differential equation, existence and uniqueness results, approximate solution.