Existence and uniqueness of solutions of infinite systems of semilinear parabolic differential-functional equations in arbitrary domains in ordered banach spaces

✍ Scribed by S. Brzychczy

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 530 KB
• Volume: 36
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(02)00268-6

✦ Synopsis

We consider the Fourier first initial-boundary value problem for a weakly coupled infinite system of semilinear parabolic differential-functional equations of reaction-diffusion type in arbitrary (bounded or unbounded) domain. The right-hand sides of the system are functionals of unknown functions of the Volterra type. DifferentiM-integral equations give examples of such equations. To prove the existence and uniqueness of the solutions, we apply the monotone iterative method. The underlying monotone iterative scheme can be used for the computation of numerical solution.