Unique continuation for parabolic equations

Journal Article · Mon Dec 30 23:00:00 EST 1996 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309608821195· OSTI ID:441145

Poon, Chi-Cheung ^[1]

---

1. National Chung Cheng Univ., Chiayi (Taiwan, Province of China)

Let u be a solution of the heat equation (1.1) {partial_derivative}u/{partial_derivative}t = {triangle}u + {sigma}{sup n}{sub i=l} b{sub i}(x,t) {center_dot} {partial_derivative}u/{partial_derivative}x{sub i} + c(x,t)u for x {epsilon} R{sup n} and t > 0. Let c and b = b{sub 1},b{sub 2},...,b{sub n} be uniformly bounded functions, i.e., (1.2) sup{sub x{epsilon}R{sup n},t>0} {parallel}c(x,t){parallel} + {parallel}b(x,t){parallel} {le} M for some constant M > 0. We will show Theorem 1.1. Suppose that both u and {triangledown}u are uniformly bounded. If u vanishes of infinite order in space-time at any point in R{sup n} X (0,{infinity}), then u is identically zero.

• Sponsoring Organization: USDOE
• OSTI ID: 441145
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 3-4 Vol. 21; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
ANALYTICAL SOLUTION
BOUNDARY CONDITIONS
HEAT TRANSFER
PARTIAL DIFFERENTIAL EQUATIONS
SPACE-TIME