Linear and Quasi-linear Equations of Parabolic Type

analogous arbitrary assume assumptions belongs boundary conditions boundary value problems bounded bounded function boundedness c₁ Cauchy problem Chapter coefficients and free conditions of Theorem consider continuous continuous function converge cylinder Q d2Zo derivatives differential domain dx dt dxdt elements equal to zero equation 1.1 finite free terms fulfilled func function u(x heat equation Hölder condition Hölder continuous Hölder's inequality identity inequality integral L₂(QT Lemma linear equations M₁ method norm obtain operator parabolic equations parameters polynomial positive number proof proved quantities respect right side satisfy conditions satisfy the conditions smooth function solution of problem solution u(x space Suppose t₁ Theorem 6.1 tion unique solvability valid vector virtue vrai max αλ ατ Κρ μ₁ μι ди дх дхі